I've read about the soul. What does spirit mean? Is there any difference between the soul and the spirit?
The definition of soul is:
The spiritual or immaterial part of a human being or animal, regarded as immortal.
Spirit is defined as:
The nonphysical part of a person that is the seat of emotions and character; the soul.
Both of them are two synonymous English words that have the same meaning. So, there is no difference between soul and sprit in Islam.
The soul is the "nufs" in Islam which is the union of body and the spirit "rouh". When a person dies there will be the body and the spirit that leaves the body.
Nafs refers to the soul when it is in a body and Ruh (spirit) refers to the soul when it is outside the body for example in Allah's repository before the angels blow it into the body.
When verses refer to a soul outside the body, the word RUH is used, when they refer to a soul inside the body, nafs is used.
O people of the Scripture (Christians)! Do not exceed the limits in your religion, nor say of Allah aught but the truth. The Messiah 'Îsa (jesus), son of Maryam (Mary), was (no more than) a Messenger of Allah and His Word, ("Be!" - and he was) which He bestowed on Maryam (Mary) and a spirit (Ruh ) created by Him; so believe in Allah and His Messengers. Say not: "Three (trinity)!" Cease! (it is) better for you. For Allah is (the only) One Ilah (God), glory be to Him (Far Exalted is He) above having a son. To Him belongs all that is in the heavens and all that is in the earth. And Allah is All-Sufficient as a Disposer of affairs. (سورة النساء, An-Nisaa, Chapter #4, Verse #171)
Narrated 'Abdullah bin Mus'ud: Allah's Apostle (SAWS), the true and truly inspired said, "(The matter of the Creation of) a human being is put together in the womb of the mother in forty days, and then he becomes a clot of thick blood for a similar period, and then a piece of flesh for a similar period. Then Allah sends an angel who is ordered to write four things. He is ordered to write down his (i.e. the new creature's) deeds, his livelihood, his (date of) death, and whether he will be blessed or wretched (in religion). Then the soul is breathed into him. So, a man amongst you may do (good deeds till there is only a cubit between him and Paradise and then what has been written for him decides his behavior and he starts doing (evil) deeds characteristic of the people of the (Hell) Fire. And similarly a man amongst you may do (evil) deeds till there is only a cubit between him and the (Hell) Fire, and then what has been written for him decides his behavior, and he starts doing deeds characteristic of the people of Paradise." (Sahih Bukhari, Book #54, Hadith #430)
This question deserves a comprehensive answer, far deeper than the probable expectation of the OP. So here is a substantial study of soul and spirit in the Quran and Sunnah. I should say I draw upon the explanations by Allama Seyyed Muhammad Hussain Tabataba'i, a great scholar, exegete and mystic of Islam in interpretation of the verses and hadiths. If you want the conclusions of this lengthy analysis skip to the Summary.
In the Quran, the relevant words are either nafs (نفس) or ruh (روح). Nafs in Quranic context means "self" or "person". But there are verses that imply that human self is indeed non-physical, therefore nafs is also usually translated to "soul".
وَ نَفْسٍ وَمَا سَوَّاهَا فَأَلْهَمَهَا فُجُورَهَا وَتَقْوَاهَ
And by nafs and He who proportioned it and inspired it with its vice and piety (91:7-8)
The verse means that Allah enlightened the self on what is right and wrong. But since the concept of ilham or inspiration is used, and since inspiration is a spiritual action, we can conclude the self is also non-physical in the eyes of the Quran, so "soul" can also be a fair translation of the Arabic word nafs. Quran also suggests that nafs survives bodily death implying that it is a non-physical thing:
يَوْمَ تَجِدُ كُلُّ نَفْسٍ مَا عَمِلَتْ مِنْ خَيْرٍ مُحْضَرًا وَمَا عَمِلَتْ مِنْ سُوءٍ تَوَدُّ لَوْ أَنَّ بَيْنَهَا وَبَيْنَهُ أَمَدًا بَعِيدًا وَيُحَذِّرُكُمُ اللَّهُ نَفْسَهُ وَاللَّهُ رَءُوفٌ بِالْعِبَادِ
The day every nafs will find what it has done of good present and what it has done of evil, it will wish that between itself and that [evil] was a great distance. And Allah warns you of Himself, and Allah is Kind to [His] servants." (3:30)
Now let's look at the context of "ruh" in the Quran which is usually translated to "spirit. In reference to a famous conversation between the non-Muslims and the Prophet (pbuh) who ask him about الروح or "the Spirit" Allah says:
وَيَسْأَلُونَكَ عَنِ الرُّوحِ قُلِ الرُّوحُ مِنْ أَمْرِ رَبِّي وَمَا أُوتِيتُمْ مِنَ الْعِلْمِ إِلَّا قَلِيلًا
They ask you of the Spirit, say the Spirit is of my Lord's command. (17:85)
Here it is obvious that there is talk of one particular being called "the Spirit" and that which belongs to "the Lord's command". In the light of another relevant Quranic verse that says Allah's command "is only one",
وَمَا أَمْرُنَا إِلَّا وَاحِدَةٌ كَلَمْحٍ بِالْبَصَرِ
And our command is except one, like a flash of eye. (54:50)
and extensive analysis of Quranic verses on amr or "command", Allama Tabatab'i' concludes that the verses correlate with the reference to the spirit in singular form. The Spirit is one, and so is the Divine command that is the source of the Spirit. We shall see another reference to "the Spirit" in Surat al-Qadr.
But now we look at other references to "spirit" in the Quran. There is talk of a "holy spirit" in the Quran who supports Prophet Isa (pbuh):
وَلَقَدْ آتَيْنَا مُوسَى الْكِتَابَ وَقَفَّيْنَا مِنْ بَعْدِهِ بِالرُّسُلِ وَآتَيْنَا عِيسَى ابْنَ مَرْيَمَ الْبَيِّنَاتِ وَأَيَّدْنَاهُ بِرُوحِ الْقُدُسِ...
And We did certainly give Moses the Torah and followed up after him with messengers. And We gave Jesus, the son of Mary, clear proofs and supported him with the Holy Spirit... (2:87)
And there is a verse that says Jesus (pbuh) was himself a spirit from Allah:
يَا أَهْلَ الْكِتَابِ لَا تَغْلُوا فِي دِينِكُمْ وَلَا تَقُولُوا عَلَى اللَّهِ إِلَّا الْحَقَّ إِنَّمَا الْمَسِيحُ عِيسَى ابْنُ مَرْيَمَ رَسُولُ اللَّهِ وَكَلِمَتُهُ أَلْقَاهَا إِلَى مَرْيَمَ وَرُوحٌ مِنْهُ فَآمِنُوا بِاللَّهِ وَرُسُلِهِ ...
O people of the Scripture! Do not exceed the limits in your religion, nor say of Allah aught but the truth. The Messiah Isa, son of Maryam, was a Messenger of Allah and His Word, which He bestowed on Maryam and a spirit from Him; so believe in Allah and His Messengers... (4:171)
Now could this spirit be possibly the same spirit Allah described as "from His command"? And is this the same "holy spirit" that later supported Jesus (pbuh) himself in his ministry?
And there is reference to the Holy spirit bringing down the revelation:
قُلْ نَزَّلَهُ رُوحُ الْقُدُسِ مِنْ رَبِّكَ بِالْحَقِّ لِيُثَبِّتَ الَّذِينَ آمَنُوا وَهُدًى وَبُشْرَى لِلْمُسْلِمِينَ
Say, "The Holy Spirit has brought it down from your Lord in truth to make firm those who believe and as guidance and good tidings to the Muslims." (16:102)
And a Trustworthy one doing the same:
وَإِنَّهُ لَتَنْزِيلُ رَبِّ الْعَالَمِينَ / نَزَلَ بِهِ الرُّوحُ الْأَمِينُ
And indeed it is a revelation from the Lord of the worlds. The Trustworthy Spirit brought it down.(192-26:193)
These verses suggest that the Trustworthy Spirit and the Holy Spirit are one and the same thing as they are said to carry out the same function of revelation. And we would have to conclude it is the same spirit that supported Prophet Isa (pbuh) as Holy Spirit is also mentioned in Jesus's context.
But these verses also raise the question of whether the Holy or the Trustworthy spirit is the same as Jibra'il, the angel most famously associated with revelation.
But there are verses that distinguish between angels in general and the spirit. In Surat al-Qadr we read:
بِسْمِ اللَّـهِ الرَّحْمَـٰنِ الرَّحِيمِ إِنَّا أَنزَلْنَاهُ فِى لَيْلَةِ الْقَدْرِ ﴿١﴾ وَمَا أَدْرَاكَ مَا لَيْلَةُ الْقَدْرِ ﴿٢﴾ لَيْلَةُ الْقَدْرِ خَيْرٌ مِّنْ أَلْفِ شَهْرٍ ﴿٣﴾ تَنَزَّلُ الْمَلَائِكَةُ وَالرُّوحُ فِيهَا بِإِذْنِ رَبِّهِم مِّن كُلِّ أَمْرٍ ﴿٤﴾ سَلَامٌ هِىَ حَتَّىٰ مَطْلَعِ الْفَجْرِ ﴿٥﴾
Indeed, We sent the Qur'an down during the Night of Decree. (1) And what can make you know what is the Night of Decree? (2) The Night of Decree is better than a thousand months. (3) The angels and the Spirit descend therein by permission of their Lord with all command. (4) Peace it is until the emergence of dawn. (5)
Here Allah says angels descend along with the Spirit. This apparently suggests that spirit is different than all other angels including Jibra'il. Also note the association with amr or command. In Surat an-Nahl there is a similar clue:
يُنَزِّلُ الْمَلَائِكَةَ بِالرُّوحِ مِنْ أَمْرِهِ عَلَىٰ مَنْ يَشَاءُ مِنْ عِبَادِهِ ...
He descends the angels by (or with) the Spirit from His command upon everyone from His servants He wishes... (16:2)
Hadiths by Imams of Ahl al-Bayt confirm that the Spirit is different from Gabriel and all other angels. In a narration from Usul al-Kafi of Sheikh Kulaini, a Shia hadith collector we read a conversation between Imam Jafar Sadiq and a companion:
٧٢١ / ٣. عَلِيُّ بْنُ إِبْرَاهِيمَ ، عَنْ مُحَمَّدِ بْنِ عِيسى ، عَنْ يُونُسَ ، عَنِ ابْنِ مُسْكَانَ ، عَنْ أَبِي بَصِيرٍ ، قَالَ : سَأَلْتُ أَبَا عَبْدِ اللهِ عليهالسلام عَنْ قَوْلِ اللهِ عَزَّ وَجَلَّ : ( يَسْئَلُونَكَ عَنِ الرُّوحِ قُلِ الرُّوحُ مِنْ أَمْرِ رَبِّي ) .
قَالَ : « خَلْقٌ أَعْظَمُ مِنْ جَبْرَئِيلَ وَمِيكَائِيلَ ، كَانَ مَعَ رَسُولِ اللهِ صلىاللهعليهوآلهوسلم ، وَهُوَ مَعَ الْأَئِمَّةِ ، وَهُوَ مِنَ الْمَلَكُوتِ ». 
Abi Basir said I asked Aba Abd Allah (Jafar as-Sadiq, peace be upon him) about Allah's saying: "They ask you of the Spirit, say the Spirit is of my Lord's command." He said: "It is a creature greater than Jibra'il and Mika'il. And it was with the Messenger of Allah (ص) and it is with the Imams (of Ahl al-Bayt) and it is from Malakut (Heavens). (source)
So it is very likely that the Spirit is one and the same thing with the Holy Spirit and that it somehow accompanies Jibra'il and other angels during their tasks. It also accompanies the Imams of Ahl al-Bayt according to Shia authorities.
And then there is talk of a spirit or spirits that particularly supports the pious believers:
لَا تَجِدُ قَوْمًا يُؤْمِنُونَ بِاللَّهِ وَالْيَوْمِ الْآخِرِ يُوَادُّونَ مَنْ حَادَّ اللَّهَ وَرَسُولَهُ وَلَوْ كَانُوا آبَاءَهُمْ أَوْ أَبْنَاءَهُمْ أَوْ إِخْوَانَهُمْ أَوْ عَشِيرَتَهُمْ أُولَئِكَ كَتَبَ فِي قُلُوبِهِمُ الْإِيمَانَ وَأَيَّدَهُمْ بِرُوحٍ مِنْهُ وَيُدْخِلُهُمْ جَنَّاتٍ تَجْرِي مِنْ تَحْتِهَا الْأَنْهَارُ خَالِدِينَ فِيهَا رَضِيَ اللَّهُ عَنْهُمْ وَرَضُوا عَنْهُ أُولَئِكَ حِزْبُ اللَّهِ أَلَا إِنَّ حِزْبَ اللَّهِ هُمُ الْمُفْلِحُونَ ﴿۲۲﴾
You will not find a people who believe in Allah and the Last Day having affection for those who oppose Allah and His Messenger, even if they were their fathers or their sons or their brothers or their kindred. Those - He has decreed within their hearts faith and supported them with a spirit from Him. And We will admit them to gardens beneath which rivers flow, wherein they abide eternally. Allah is pleased with them, and they are pleased with Him - those are the party of Allah. Unquestionably, the party of Allah - they are the successful. (58:22)
In the light of the above survey, we see that in all contexts "spirit" is usually associated with such functions as divine inspiration, revelation, support and intervention.
The latter verses are distinct in that they use an indefinite article to refer to 'spirit' implying that it can be different from the Holy Spirit that inspires the Prophet (pbuh). I will come back to this apparent distinction later, after one last distinguished context that talks about spirit in the Quran and that would be the human creation story:
فَإِذَا سَوَّيْتُهُ وَنَفَخْتُ فِيهِ مِنْ رُوحِي فَقَعُوا لَهُ سَاجِدِينَ
And when I proportioned him and breathed into him of My spirit, they fell down to him in prostration. (15:29)
This verse is important in that it says spirit was breathed into Adam and once it was breathed into him angels fell in prostration. So it indicates that Adam had at least a share of Allah's spirit that imbued him with a noble quality that invoked angels' respect.
In this verse human faculties arise after Allah blows into Adam His spirit:
ثُمَّ سَوَّاهُ وَنَفَخَ فِيهِ مِن رُّوحِهِ ۖ وَجَعَلَ لَكُمُ السَّمْعَ وَالْأَبْصَارَ وَالْأَفْئِدَةَ ۚ قَلِيلًا مَّا تَشْكُرُونَ
Then He proportioned him and breathed into him from His spirit and made for you hearing and vision and hearts; little are you grateful. (32:9)
These verses are important in that they highlight the spirit's role in creation and their association with consciousness. Adam's creation via Divine spirit parallels the story of Prophet Isa's birth who is described as "a spirit from Him [Allah]". Here, also, spirit is used in singular form.
More information about "spirit" is contained in the hadiths by Imams of Ahl al-Bayt (pbut). These hadiths also have particular references to exclusively Shia beliefs but the additional information that they offer on the Spirit is basically consistent with information from the Quran:
عَنْ جابر عَنْ أَبِي جَعْفَرٍ عليهالسلام ، قَالَ : سَأَلْتُهُ عَنْ عِلْمِ الْعَالِمِ ، فَقَالَ لِي : « يَا جَابِرُ ، إِنَّ فِي الْأَنْبِيَاءِ وَالْأَوْصِيَاءِ خَمْسَةَ أَرْوَاحٍ : رُوحَ الْقُدُسِ ، وَرُوحَ الْإِيمَانِ ، وَرُوحَ الْحَيَاةِ ، وَرُوحَ الْقُوَّةِ ، وَرُوحَ الشَّهْوَةِ ، فَبِرُوحِ الْقُدُسِ يَا جَابِرُ ، عَرَفُوا  مَا تَحْتَ الْعَرْشِ إِلى مَا تَحْتَ الثَّرى  ».
Jabir said I asked Abi Jafar (Imam Muhammad al-Baqir, peace be upon him) about knowledge of the knowledgeable, and he told me: O Jabir! In Prophets and Vicegerents there are five spirits: the Holy Spirit, the Spirit of faith, the Spirit of life, the Spirit of power, and the Spirit of desire. And by the Holy Spirit they know whatever is under the Throne all the way to what is under the dust.
ثُمَّ قَالَ : « يَا جَابِرُ ، إِنَّ هذِهِ الْأَرْبَعَةَ أَرْوَاحٌ يُصِيبُهَا الْحَدَثَانُ  إِلاَّ رُوحَ الْقُدُسِ ؛ فَإِنَّهَا لَا تَلْهُو  وَلَاتَلْعَبُ ».  (source)
Then said: O Jabir, these four spirits are affected by incidences except the Holy Spirit who doesn't act in vain or play.
عَنِ الْمُفَضَّلِ بْنِ عُمَرَ : عَنْ أَبِي عَبْدِ اللهِ عليهالسلام ، قَالَ : سَأَلْتُهُ عَنْ عِلْمِ الْإِمَامِ  بِمَا  فِي أَقْطَارِ الْأَرْضِ وَهُوَ فِي بَيْتِهِ مُرْخًى  عَلَيْهِ سِتْرُهُ. فَقَالَ : « يَا مُفَضَّلُ ، إِنَّ اللهَ ـ تَبَارَكَ وَتَعَالى ـ جَعَلَ فِي النَّبِيِّ صلىاللهعليهوآلهوسلم  خَمْسَةَ أَرْوَاحٍ : رُوحَ الْحَيَاةِ ، فَبِهِ دَبَّ وَدَرَجَ  ؛ وَرُوحَ الْقُوَّةِ ، فَبِهِ نَهَضَ  وَجَاهَدَ ؛ وَرُوحَ الشَّهْوَةِ ، فَبِهِ أَكَلَ وَشَرِبَ وَأَتَى النِّسَاءَ مِنَ الْحَلَالِ ؛ وَرُوحَ الْإِيمَانِ ، فَبِهِ آمَنَ  وَعَدَلَ ؛ وَرُوحَ الْقُدُسِ ، فَبِهِ حَمَلَ النُّبُوَّةَ ؛ فَإِذَا قُبِضَ النَّبِيُّ صلىاللهعليهوآلهوسلم انْتَقَلَ رُوحُ الْقُدُسِ ، فَصَارَ إِلَى الْإِمَامِ ، وَرُوحُ الْقُدُسِ لَايَنَامُ وَلَايَغْفُلُ  وَلَايَلْهُو وَلَايَزْهُو  ، وَالْأَرْبَعَةُ الْأَرْوَاحِ تَنَامُ وَتَغْفُلُ وَتَزْهُو وَتَلْهُو  ، وَرُوحُ الْقُدُسِ كَانَ  يَرى بِهِ  ». وفي البصائر : « و روح القدس ثابت يرى به ما في شرق الأرض وغربها ، وبرّها وبحرها.
Mufazzal ibn Umar said I asked Abi Abd Allah (Imam Jafar Sadiq) about awareness of the Imam about everything around the Earth while he is covered in his home. He said: O Mufazzal, Allah the Merciful and the High, put five spirits in the Prophet (pbuh): the spirit of life by which he moves and walks, the spirit of power by which he rises and struggles, the spirit of desire by which he eats, drinks, make lawful wives, and the spirit of faith by which he finds faith and acts justly, and the Holy Spirit by which he carries the prophethood. And once the Prophet dies, the Holy Spirit moves to the Imam, and the Holy Spirit doesn't sleep or forget or act in vain or arrogance, and by the Holy Spirit he sees. (source)
What is said of the Holy Spirit's relation to the Prophet of Islam in these hadiths is consistent with what Quran says of the Holy Spirit. Another hadith says that all spirits except the Holy Spirit exist in the the faithful, "the people of the right hand":
وَجَعَلَ فِي الْمُؤْمِنِينَ ـ أَصْحَابِ  الْمَيْمَنَةِ ـ رُوحَ الْإِيمَانِ ، فَبِهِ خَافُوا اللهَ ؛ وَجَعَلَ فِيهِمْ رُوحَ الْقُوَّةِ ، فَبِهِ قَدَرُوا  عَلى طَاعَةِ اللهِ ؛ وَجَعَلَ فِيهِمْ رُوحَ الشَّهْوَةِ ، فَبِهِ اشْتَهَوْا طَاعَةَ اللهِ ؛ وَجَعَلَ فِيهِمْ رُوحَ الْمَدْرَجِ الَّذِي بِهِ يَذْهَبُ النَّاسُ وَيَجِيئُونَ  ». 
And Allah put in the believers, the people of the right hand, the spirit of faith by which they fear Allah, and spirit of power by which they are enabled to obey Allah, and spirit of desire by which they desire obedience of Allah, and the spirit of motion by which they come and go.
These spirits that are commonly found in believers parallel the Quranic verses that mention Allah's support for believers by "a spirit from him".
Considering all these verses and hadiths, we may conclude the following points about the Spirit, nafs and the spirits:
- Spirit is a force of life, knowledge and power which are the most essential Divine attributes. Allah manifests His wills via this lofty creature.
- Spirit is a singular encompassing being that has many emanations, levels and appearances, permeating all living beings from angels all the way to animals and plants giving them life and consciousness. That's why the Spirit can be referenced in plural or indefinite voice despite its ultimate unity, and this is the basis of multiple kinds of spirit in Quran and hadiths.
- The Spirit in its full nature is the embodiment of Allah's Beautiful Names, and that's why Adam could learn all those names when angels couldn't; for Adam was the full embodiment of the Spirit.
- From the above we also understand that the Spirit in its lofty levels manifest in prophets, saints and angels. In these cases the spirit is usually described as "holy" because in its lofty stations it doesn't mix with inferior creatures or ordinary human souls.
- The lower levels of the Spirit manifest itself in all worldly living beings. Human soul or nafs and its faculties such as mind, senses and desires are lowermost manifestations of the spirit. This is corroborated by the verse that says Allah created humans from "nafsin wahida", a single nafs, but we know that we all have our own individual nafs. So it has to be that the Soul despite its unity can have multiple (indeed infinite) manifestations, and human souls are the multiple manifestations of the one Spirit. Hence humans can be said to be from one nafs despite being many.
هُوَ الَّذِي خَلَقَكُم مِّن نَّفْسٍ وَاحِدَةٍ وَجَعَلَ مِنْهَا زَوْجَهَا لِيَسْكُنَ إِلَيْهَا
It is He who created you from one soul and created from it its mate that he might dwell in security with her (7:189)
However, like said, not all individuals can fully incarnate the Spirit. Only Prophets and Awliya can achieve this. Not even angels can fully incarnate the Spirit as they have admitted that they have a fixed station:
"وَمَا مِنَّا إِلَّا لَهُ مَقَامٌ مَعْلُومٌ (164) وَإِنَّا لَنَحْنُ الصَّافُّونَ (165)"
There is not of us except with a defined station. And indeed we are in ranks.
That's why Adam is superior to them and that's why they needed to prostrate before him. That's also why the Prophet of Islam could excel over Jibra'il in his spiritual ascension Miraj.
It is by the gradual and modest outplay of the Spirit that creatures are enlivened with life through the normal process of procreation and growth in the world, whereas it is by its forceful and special manifestation that miracles take place such as conception of Prophet Isa (pbuh) in Lady Maryam (pbus) without human intercourse, or enlivening of the Moses's stick or the Jesus's clay bird statue. The case of Jesus literally blowing his breath to enliven a clay bird indicates that even human natural breath is a manifestation of the Divine spirit which enlivened Adam. But Jesus' breath in particular carries particularly mighty levels of the Spirit enabling it to give life to dead objects.
The above account of the spirit whose basic outline has been presented by Allama Tabataba'i has admittedly deeply fascinated me for its explanatory power and far reaching implications. In it I also see parallels with some aspects of the Christian account of the Holy Spirit and its unity with God and Jesus (apart from its wrongful deification of Jesus and connotations for trinity), the concept of Atman and its relation to Brahman in Hindu Religion, the New Age concept of Universal Consciousness, and the Cosmic Consciousness postulated by some psychologists who study religious experience. The concepts coming from different cultures and groups seem to be attempts to express encounter with an all-encompassing life force with similar characteristics.
Thanks to Allah for relaying us His wisdom via His Prophets and Saints