The fast of Ramadan is one of the "five pillars of Islam" and a principal precept of the faith. Muslims are commanded to fast from sunrise to sunset for the whole month. It is customary, during the month of Ramadan, to read the whole entire Qur'an, usually broken down into 30 units, one per day of the month.
The commandment to fast is mentioned in various parts of the Qur'an, for example in the following verse:
"شَہۡرُ رَمَضَانَ ٱلَّذِىٓ أُنزِلَ فِيهِ ٱلۡقُرۡءَانُ هُدً۬ى لِّلنَّاسِ وَبَيِّنَـٰتٍ۬ مِّنَ ٱلۡهُدَىٰ وَٱلۡفُرۡقَانِ فَمَن شَہِدَ مِنكُمُ ٱلشَّہۡرَ فَلۡيَصُمۡهُ وَمَن ڪَانَ مَرِيضًا أَوۡ عَلَىٰ سَفَرٍ۬ فَعِدَّةٌ۬ مِّنۡ أَيَّامٍ أُخَرَ يُرِيدُ ٱللَّهُ بِڪُمُ ٱلۡيُسۡرَ وَلَا يُرِيدُ بِڪُمُ ٱلۡعُسۡرَ وَلِتُڪۡمِلُواْ ٱلۡعِدَّةَ وَلِتُڪَبِّرُواْ ٱللَّهَ عَلَىٰ مَا هَدَٮٰكُمۡ وَلَعَلَّڪُمۡ تَشۡكُرُونَ" (سورة البقرة: 185)
"It was in the month of Ramadan that the Qur'an was revealed as guidance for mankind, clear messages giving guidance and distinguishing between right and wrong. So any of you who is present that month should fast, and anyone who is ill or on a journey should make up for the lost days by fasting on other days later. God wants ease for you, not hardship. He wants you to complete the prescribed period and to glorify Him for having guided you, so that you may be thankful."
[M.A.S. Abdel Haleem, The Qur'an (Oxford: Oxford University Press, 2004)]
For the believer, the month of Ramadan is a time of introspection, spiritual catharsis, and intensification of piety and faith. It is customary to increase charitable contributions (another one of the "five pillars of Islam") since, according to Muslim tradition, charity given during Ramadan is more of a credit to the benefactor than charity given at other times. Ramadan is also a month devoted to family and society and many open their homes for the evening meal, welcoming guests and visiting relatives, neighbors and friends.
Towards the end of Ramadan the Laylat al Qadr ("Night of Destiny" or "Night of Power") is celebrated. According to the Qur'an, on this night Mohammed had his first revelation. Muslim tradition holds that Allah decides the fate of all people on this night. Therefore, the religious custom is to add extra prayers on the last ten days of the month and to pray as much as possible on the Night of Destiny itself. Those who are able to, spend the ten days in the Mosque, night and day, praying and reading from the Qur'an – a custom known as I’tikaf. According to one tradition, the Night of Destinyfalls the 27th day of the month, while others observe it on the 21st, 23rd, 25th, or 29th of the month. Thus, the Night of Destiny can occur on any odd day during the last ten days of Ramadan.
Laylat al Qadr is mentioned in Surat al Qadr:
"إِنَّآ أَنزَلۡنَـٰهُ فِى لَيۡلَةِ ٱلۡقَدۡرِ (١) وَمَآ أَدۡرَٮٰكَ مَا لَيۡلَةُ ٱلۡقَدۡرِ (٢) لَيۡلَةُ ٱلۡقَدۡرِ خَيۡرٌ۬ مِّنۡ أَلۡفِ شَہۡرٍ۬ (٣) تَنَزَّلُ ٱلۡمَلَـٰٓٮِٕكَةُ وَٱلرُّوحُ فِيہَا بِإِذۡنِ رَبِّہِم مِّن كُلِّ أَمۡرٍ۬ (٤) سَلَـٰمٌ هِىَ حَتَّىٰ مَطۡلَعِ ٱلۡفَجۡرِ (٥)" (سورة القدر)
"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 for every matter. (4) Peace it is until the emergence of dawn. (5)"
[Qur'an Sura 97:1-5 (http://Qur'an.com/97/
This year, the Night of Destiny, Laylat al Qadr, falls on the 13,14 or 15 of August, depending on location. Like all festivals in Islam, it depends on observation of the moon.