From the Lailat al-Qadr Wikipedia page:
Laylat al-Qadr (Arabic: لیلة القدر) (also known as Shab-e-Qadr , loaned from Persian), variously rendered in English as the Night of Decree, Night of Power, Night of Value, Night of Destiny, or Night of Measures, is in Islamic belief the night when the first verses of the Quran were revealed to the Islamic prophet Muhammad. It is one of the odd nights of the last ten days of Ramadan. Muslims believe that on this night the blessings and mercy of Allah are abundant, sins are forgiven, supplications are accepted, and that the annual decree is revealed to the angels who also descend to earth.
Muslims believe that Laylat al-Qadr was the night when the Quran was revealed to Muhammad from Allah. Most Muslims believe that revelation of the Quran occurred in two phases, with the first phase being the revelation in its entirety on Laylat al-Qadr to the angel Gabriel (Jibril in Arabic) in the lowest heaven, and then the subsequent verse-by-verse revelation to Muhammad by Gabriel, across 23 years. The revelation started in 610 CE at the Hira cave on Mount Nur in Mecca. The first Sura that was revealed was Sūrat al-ʿAlaq (in Arabic العلق). During the first revelation the first five verses of this Sura, or chapter, were revealed.
Muslims often offer extra prayers, particularly the night prayer. They hold a vigil, pray, seek Allah's forgiveness and mercy, and hope that their supplications will be accepted on this night. Mostly, they perform tilawat (reading the Quran).
Those who can afford to devote their time in remembrance of Allah stay in the mosque for the final ten days of Ramadan. This worship is called Iʿtikāf (retreat). They fast during the day and occupy themselves with the remembrance of Allah, performing voluntary prayers and studying the Quran, day and night, apart from the obligatory prayers which they perform with the congregation. Food and other necessities of life are provided for them during their stay in the mosque. By devoting time to remember Allah, Muslims also hope to receive divine favors and blessings connected to Laylat al-Qadr.