Recently I heard the term 'Wahhabism' for specifying a group of Muslims. Actually what is Wahhabism? Is it a sect or normal religious group?
Abdullah (previously Ershad) has explained the Wahhabi movement from the Wahhabi perspective and has mentioned some nice and positive aspects of the Wahhabi movement.
Every group believes that they are right, often they believe they are completely right with no mistake in their beliefs. Typically it is almost impossible to find any serious criticism or discussion of negative aspects and facts about the group in their own writings. Let me try to provide a perspective from outside the movement. Hopefully together with Abdullah's answer we will have a more objective view of the movement.
Please keep in mind that some of what I write below only applies to more radical groups in the Wahhabi movement and may not be correct/accurate about more moderate Wahhabi Muslims.
The Wahhabi movement is a recent 18th century ultraconservative fundamentalist movement inside the Salafi movement. It was initiated by Muhammad ibn Abd al-Wahhab. The followers of this branch dislike being called "Wahhabi" because it designates them as followers of the teachings of Muhammad ibn Abd al-Wahhab which is harmful to their claim that they are the true followers of the true Islam.
Wahhabi movement is typically associated with Saudi Arabia, since historically it started there in the 18th century, became dominant through alliance with Al Saud family, it is the dominant practice of Islam in Saudi Arabia, and it is strongly supported and promoted by the Saudi government. The cost of the alliance was that the Wahhabi leaders should leave the political space to the Al Saud family. Therefore the Wahhabi movement often discourages its followers from participating in political process (like elections, popular protests, etc.). Looking at the early Islamic history it seems that discouraging political participation is not based on early Muslim society but rather an addition for the sake of the alliance between Wahhabi leaders and Al Saud family. This apolitical attitude sometimes changes, e.g. extremist Wahhabi groups like Taliban, ISIS, etc. try to revive the Islamic Caliphate through force and violence, and sometimes peacefully like the Wahhabi movement in Egypt which initially were against any participation in elections and protests against Mobarak, but changed their view after the Mobarak was toppled and participated in the elections as the Al-Nour party.
The movement has a nostalgic and romantic view of the early Muslim society and the first three generations of Muslims. This idealization of Islamic society and early Muslims makes them intolerant of practices not conforming to their understanding. They believe it is possible to have a perfect Muslim society by emulating the early Islamic society. Anything after that period is considered with suspension and sometimes as corruption. This is more true about those periods of Muslim history where leaders of Muslims were not Arabs (essentially anything after the Umayyad period, and specially the Ottoman period). There are some elements of pan-Arabism in the movement.
Sometimes the Wahhabi movement is categorized under Hanbali school of Islamic jurisprudence (figh). The movement started among Muslims following Hanbali school and its growth so far has been mainly among the followers of Hanbali school. But the movement is growing among other Sunni jurisprudence schools (which have been considered more tolerant than Hanbali school).
The Wahhabi movement's strong insistence that they are following the true Islam comes with a strong insistence that other Muslims are not following the true Islam. This makes them intolerant of other Muslims when they seem to disagree with Wahhabi teachings. This originates from their belief that unlike other schools they are not interpreting Islamic sources and their understanding of Islamic sources is just Islam and nothing more. They typically have a literal reading of Islamic sources. In particular they have a very strict understanding of "tawheed (monotheism)" and do not tolerate those who disagree with their understanding. You can literally loose your head for doing something that violates tawheed in their view.
They consider followers of other branches of Islam to be "mushrik". They have a strong anti-Shia and anti-Sufi attitude and consider them "mushrik". They also take actions against these groups by takfiring them. I should add that takfir is more than just calling someone non-Muslim, it typically has severe consequences: the takfir of a person makes him loose legal rights, loose ownership of his property, invalidate his marriage, and even gives permission to kill him as a kafir (some extremist Wahhabi groups believe that it is permitted and even duty to kill kafirs just for being kafir).
The issue gets more severe because this practice of takfir is extended to other beliefs and teachings of the movement, e.g. (as Abdullah confirmed) some Wahhabi scholars takfir those Shia Muslims who believe that some non-prophets like Ali ibn Abī Ṭālib (PBUH) are above some prophets (PBUT). There are similar cases against Sunni Muslims practicing Sufism for things like celebrating the birthdays of Sufi Muslim saints.
Wahhabi movement also destroys historical Islamic sites. You will have a very hard time finding any historical Islamic place from pre-Al Saud period in Saudi Arabia. This extends to sites associated with the prophet and his family and companions. All of this is done in the name of fighting "shirk". Some Wahhabi scholars even want to destroy "Al-Masjid al-Nabawi" and the prophet's own tomb (see also this article in the Independent). Their justification is that some Muslims pray at these sites and seek help from these saints and ask the saints to pray for them in gaining God's favor. They understand these practices as asking favors from someone other than God and therefore "shirk". There are verses in Quran which indicate it is not problematic to ask others to pray for us in gaining God's favor. However, according to the Wahhabi understanding these verses only apply to living persons, so it is forbidden to do so if the saint has passed away and is not in this world. Again, the issue goes back on their strong insistence on a particular interpretation. By the way, there does not seem to be any evidence that the destruction of graves and historical sites that is practiced by the movement is a part of Prophet's Sunnah, nor that of the four Caliphs following him.
They are also hostile to any practices that is not based on the actions and sayings of the first three generations of Muslims. It is probably OK to say that one should not claim that any practice which is not based on Quran and sayings and actions of the prophet (and maybe early Muslims) is not part of the original Islamic teachings. However, because of their strong puritan tendencies and idealistic view of early Muslim society as the complete perfect society, they forbid such actions and teachings generally even if one makes no claim that it was part of original Islamic teachings. You are not allowed to come up with new practices acceptable in Islam by yourself. This in particular confronts the teachings of Shia and Sufi Muslims who believe that God may give new good teachings to Muslims (through Shia Imams or Sufi saints). It restricts the framework of acceptable and good practices to those during the first three generations of Muslims. It is an ultraconservative understanding of the Islam in the sense that it is not sufficient that a practice does not violate basic teachings of Islam. Anything that is not based on those basic teachings is forbidden. This seems to be against the teaching of Quran that regularly orders scholars not to forbid what God has not forbidden. In this ultraconservative reading, all such teachings are considered "innovation" (Bid'ah) and are forbidden. They also have a very strict ultraconservative static understanding of Islamic law (figh). They reject the influence of non-Arab cultures in later periods as non-Islamic, but because of their idealistic view of the first three generation of Muslims they do not make much distinction between Islamic teachings and the Arab cultural of that time. In other words, the behavior and Arab culture of Muslims during early Islamic history become part of Islam and are an ideal to be emulated, while the behavior and non-Arab culture of later periods are rejected as unIslamic and something to be avoided.
Because of these and similar issues and their general intolerance and violence towards other Muslim groups (sometimes based on small difference in beliefs, practices, or interpretations of Islamic sources) many Muslim scholars (Sunni and Shia) consider them extremists. Some scholars see similarities between the extremist Wahhabi groups and an early group in Islamic history called Kharijites (Grand Imam of Al Azhar University al Sharif Dr. Ahmed Al-Tayeb here, Grand Mufti of Egypt Ali Gomaa, some Shia scholars, and even Saudi Prince Mamdouh bin Abdulaziz). Kharijites had a very strict and ultraconservative understanding of Islam and were intolerant and violent towards other Muslims who disagreed with their interpretation (including the forth Caliph).
The estimated percentage of Muslims following Wahhabi school is relatively small (less than 4% of Muslims, mainly in the central parts of Saudi Arabia and coastal parts of United Arab Emirates).
(A larger versions of the map can be found here.)
However according to some reports, they are the fastest growing group among Muslims (this is mainly attributed to the heavy financial support by Saudi government which some estimate to provide over 90% of total money spent for preaching Islam in the world).
I am not sure what you mean by "is it a sect or normal religious group?". It is a movement and a school of thought in Islam practiced by some Muslims.
The term "Wahhabi" is nothing but an outcome of ideological attack by made by media and other sects in their efforts to harm the Call to Islamic Monotheism (Tawheed). It is sad to see some people still want to propagate this myth from what they know from hearsay information. And most probably, they even wouldn't know where the term comes from or what the so-called "wahhabis" call for.
The term "wahabbi" comes from a scholar of Islam named "Muhammad bin Abd al-Wahhaab".
The condition of the Muslims in his time was a dire one and is described by historians and by both Imaam al-Shawkani (d. 1834CE) and Imaam al-San'aanee (d. 1769CE) (both contemporaries) as one in which the people had turned to worshipping graves, stones, trees and the likes. The people had abandoned or were very lax towards the main symbols of worship (prayer, zakah) and were content with innovations which became their connection to the religion, and rare were the scholars who would enjoin the good and forbid the evil, most were content with the status quo, and those who were not content were not able to speak out due to not having the will and courage.
In this setting, Ibn Abd al-Wahhab began calling the people to the monotheism of the Prophets and Messengers, and rejected the worship of the graves, attachment to them, and soliciting intercession from them, and calling upon the dead for rescue from calamity and what is similar to this.
And for the people who say this is something new - No, it is not. Many scholars before him called people to the same thing and long before them the Prophets and the Messengers. Many scholars spoke against plastering of graves like Imam Maalik. Some people who blame him of destroying "historically important" sites/graves would like to see this hadith:
Ali Ibn Abi Talib said to abul Hayyaj al-Asadi: "Shall I charge you with a duty which the Prophet (salallahu alaihe wa-sallam) charged me with? Destroy every idol or statue and level down every raised grave." [Saheeh Muslim]
And regarding what people accuse him of rejecting Madhabs and Islamic Scholarship (without any proof), this is my proof that he didn't from his own Book, He said, as occurs in al-Durar al-Saniyyah (1/228-229):
ثم إنا نستعين على فهم كتاب الله، بالتفاسير المتداولة المعتبرة، ومن أجلها لدينا : تفسير ابن جرير، ومختصره لابن كثير الشافعي، وكذا البغوي، والبيضاوي، والخازن، والحداد، والجلالين، وغيرهم . وعلى فهم الحديث، بشروح الأئمة المبرزين : كالعسقلاني، والقسطلاني، على البخاري، والنووي على مسلم، والمناوي على الجامع الصغير . ونحرص على كتب الحديث، خصوصاً : الأمهات الست، وشروحها ؛ ونعتني بسائر الكتب، في سائر الفنون، أصولاً، وفروعاً، وقواعد، وسيراً، ونحواً، وصرفاً، وجميع علوم الأمة . ولا نأمر باتلاف شيء من المؤلفات أصلاً، إلاّ ما اشتمل على ما يوقع الناس في الشرك، كروض الرياحين، أو يحصل بسببه خلل في العقائد، كعلم المنطق، فإنه قد حرمه جمع من العلماء، على أنا لا نفحص عن مثل ذلك، وكالدلائل، إلاّ إن تظاهر به صاحبه معانداً، أتلف عليه ؛ وما اتفق لبعض البدو، في اتلاف بعض كتب أهل الطائف، إنما صدر منه لجهله، وقد زجر هو، وغيره عن مثل ذلك .
Thereafter, we seek aid in understanding the Book of Allaah with the well-circulated, accepted books of tafseer (Qur’anic commentary), and from the loftiest of them in our view are the tafseer of Ibn Jarir, and its summarized version by Ibn Kathir al-Shafi’i, and likewise (that of) al-Baghawi, and al-Baydawi, and al-Khaazin, and al-Haddaad and al-Jalaalayn and other than them.
And in understanding the hadeeth, with the explanations upon [the hadeeth collection of] al-Bukhari by the prominent scholars such as al-Asqalaani, al-Qastalaani. And [that of] al-Nawawi for [the hadeeth collection of] Muslim, and [that of] al-Munawi upon al-Jami’ al-Sagheer. And we are eager for the books of hadeeth, such as the six main books and their explanations, and we are occupied with all of the books, in all of the various disciplines, both in the foundations and the subsidiary [matters], in the principles, in biographies, in grammar, morphology and in all of the sciences of this Ummah.
And we do not command the destruction of any of the authored works at all except what comprises that which makes the people fall into polytheism, such as Rawd al-Riyaaheen, or [those books] on account of which errors in creed are acquired, such as [books] on [Greek] logic, for a group of the Scholars have prohibited them, bearing in mind that we do not investigate into such matters (in any case), and like [the book] al-Dalaa’il. [And the same is with any book] unless its author manifests obstinacy [with respect to what is in it of error and misguidance], in that case it is destroyed.
And as for what one of the Bedouins did of destroying some of the books of the people of al-Taa’if, then that occurred from him due to his ignorance, and he and others have been reprimanded from the likes of that.
Shaykh Muhammad ibn ‘Abd al-Wahhaab said, describing himself, was:
“I tell you that– praise be to Allah – my belief and my religion, according to which I worship Allah, is the way of Ahl al-Sunnah wa’l-Jamaa’ah, which was the way of the imams of the Muslims, such as the four Imams and their followers until the Day of Resurrection. But I explain to people that they must devote their worship sincerely to Allah (ikhlas). I forbid them to call upon the Prophets and the dead among the righteous and others, and from associating them with Allah in any act of worship that should be done for Allah alone, such as offering sacrifices, making vows, putting one’s trust, prostrating and other actions which are due to Allah and in which no one should be associated with Him, not any angel who is close to Him or any Prophet who was sent. This is the Message which was proclaimed by all the Messengers, from the first of them to the last of them, and this is the way of Ahl al-Sunnah wa’l-Jamaa’ah. I hold a high position in my village and people listen to me. Some of the leaders denounced that because it goes against the customs they grew up with. I also obliged those who are under me to perform regular prayer, pay zakaah and fulfil other Islamic duties, and I forbade them to deal with ribaa, drink intoxicants and other kinds of forbidden things. The leaders could not criticize that or find fault with it, because it is something that is liked by the common folk, so they directed their criticism and enmity against that which I enjoin of Tawheed and that which I forbid of shirk, and they confused the common folk by saying that this goes against what everyone is doing, and they caused a great deal of fitnah…” (al-Durar al-Sanniyyah, 1/64-65, 79-80)
So he never rejected Islamic scholarship rather he encouraged to take from them and note the bold part The four Imams refers to the four madh-habs.
His call was not a new call and nor an innovated call for he was preceded in this rejection [of Worshiping graves] by centuries by other scholars such as Ibn Aqeel (d. 488H) and Ibn al-Jawzee (d. 597H), both Hanbalis, and the erroneous nature of these practices was even indicated by Fakhr al-Din al-Razi (d. 606H) - see this article and likewise al-Maqrizi (d. 845H), the Shafi'i scholar from Egypt (see this article). His call started in Huraymalah, then went to al-Uyainah where he won temporary support of Uthmaan bin Mu'ammar, and then al-Dir'iyyah where he won the support of the leader, Muhammad bin Sa'ud, who had accepted his call.
You should listen to his complete biography explained in this audio.
Muhammad bin Abd al-Wahhaab wrote many books on Tawheed because his focus was on the Monotheism and he was trying to revive it. His interest was to remove shirk (polytheism) which was what the call of the Prophet himself. His books include Kitab at-Tawheed (Book of Monotheism), Kashf ush-Shubuhaat (Removal of Doubts), Masaa’il-ul-Jaahiliyyah(Aspects of the days of Ignorance) and much more. All surrounded the central theme of "Tawheed" (Monotheism).
And one more allegation is made by some people is that the Terrorists and Extremists follows the principles of Muhammad bin Abd al-Wahhaab. These are merely empty claims. These Myths are debunked by scholars and students of knowledge umpteen times in a detailed manner. You can read a detailed article here about the "Wahhabi" Myth and the complete debunking of it. This fact is also mentioned in Encyclopedia of World Biography:
Some have alleged that his strict interpretation of Islam has motivated terrorist activities generally and has specifically formed the basis for the militant Islam of terrorist mastermind Osama bin Laden, a Saudi follower of Wahhabism. During his own lifetime, however, Ibn Abd al-Wahhab favored debate and religious instruction over violent campaigns as methods of persuasion, and the proposed link between bin Laden and Wahhab’s thought has encountered strenuous objections.
[Abd al-Wahhab, Muhammad Ibn (c. 1702-c. 1791)." Encyclopedia of World Biography. Vol. 27. Detroit: Gale, 2007]