I know that the Qur'an is the book revealed by the prophet Muhammad, but I'd like to know what the meaning of this word "Qur'an" is literally? What is its root?
Beside the well known and among Muslims preferred meanings already explained here "The recitation" or "the continuous recitation" there are others one should know:
Of course if we assume that قرآن comes from the verb "قرأ" then it would be a superlative and would mean: intensely read/recited (as reading is also understood in the case of Quran as reciting) -as you may find in the nice comment of @Shoaib (user549)-!
The word قرآن Quran is derived from "قرأ"،"يقرأ"،"قراءة"،و"قرآنا" with the origin "القَرء" which means the merged or joint (or even collected). The Quran has been named so because its joint the Verses and Suwar with each other. (See for example in lessan al-'Arab)
Some (al-Farra') said قرآن is derived from القرائن the associates or mates, because one Verse in it is similar to an other and one confirms an other!
Imam a-Shafi'i said
القرآن اسم وليس بمهموز ولم يؤخذ من قرأت، ولكنه اسم لكتاب الله
The Quran is a noun without a hamza and he is not derived from قرأت (i read) but it's the name of the book of Allah
One should know that Imam a-Shafi'i grow up in Mekka and the Qira'a of Mekka (the Qira'a of ibn Kathir, whom a-Shafi might have been a direct (narrator) student of) always pronounces the word قرآن without hamza "ء" in the middle "قران".
Also note that the Arabs of the tribe Quraish where rather rarly emphasizing an alif with a hamzah as it is the case for the tribe of Hudail. Therefore the Kufi qira'at -like Hafs 'an 'Asim- which have been influenced a lot by ibn Masu'd include a lot more hamzah than any others.
Orientalists tend to say that the word is derived from the Syriac word قريانا Quryana which means read (or study) the holy book.
Because of the relation between Hebrew and Arabic (Same Aramaic origin, which is even earlier than the Syriac!) one may also consider The ancient name of Torah = Mikra,מקרא, مقرا, as the Masdar/Origin مقرا is directly formed by adding the prefix م to قرأ. This is the standard pattern for forming nouns from verbs in Arabic. Makra means "that which is read," which is the same as Quraan and Mikra (Torah). One can therefore conclude that Quraan is the name of the previous books as well as the final book of God (See comment of @Shoaib).
And Allah knows best
the meaning is "Continous Recitation" and not only "recitation". Qira means = Recitation Quran means = Continous recitation.
Mad on top of Alif makes a meaning of umbrella or sky or continuous. The later is more correct.
Adding Al in the beginning of Quran, changes the meaning in classical Arabic, it becomes "The book which is to be recited continuously" OR "the book which is to be recited" howver classical Arabic explains Quran "continuous recitation".