Laylat al-Qadr (Arabic: لیلة القدر) (also known as Shab-e-Qadr), basically the Night of Decree or Night of Measures, is the anniversary of two very important dates in Islam that occurred in the month of Ramadan. It is the anniversary of the night Muslims believe the first verses of the Qur'an were revealed to Prophet Muhammad.
Shia Muslims believe also that this night is when their fate in the following year is decided and hence pray for God all night long and pray for mercy and salvation. This practice is called Ehyaa (basically meaning "revival").
Complete revelation to Muhammad
Laylat al-Qadr is the anniversary of the night Muslims believe the first verses of the Qur'an were revealed to Prophet Muhammad by the angel Gabriel (Jibril in Arabic). It is also the anniversary of the night in which the Qur'an is believed by Muslims to have been revealed in its entirety. The Laylat al -Qadr can also be known as the night of excellence.
Religious importance Of Muhammad
(Qur'an 97, 1-5) 
In the name of God, the Benevolent, the Merciful.1 Lo! We revealed it on the Night of Predestination.2 Ah, what will convey unto thee what the Night of Power is!3 The Night of Power is better than a thousand months.4 The angels and the Spirit descend therein, by the permission of their Lord, with all decrees.5 (The night is) Peace until the rising of the dawn.
The verses above regard the Night as better than one thousand months. The whole month of Ramadan is a period of spiritual training wherein believers devote much of their time to fasting, praying, recitating the Qur'an, remembering God, and giving charity. However because of the revealed importance of this night, Muslims strive harder in the last ten days of Ramadan since the Laylat al-Qadr could be one of the odd-numbered days in these last ten (the first, third, fifth, or seventh). Normally, Muslims would perform an i'tikaf in the mosque (i.e they remain in the mosque for the last ten days at a strech) for prayers and recitation.
Muslims often pray extra prayers on this day, particularly the night prayer. They awake, pray, and hope Allah will give them anything they may desire for on this night. Mostly, they perform tilawat (reading the Qur'an).
Those who can afford to devote their time in the remembrance of God stay in the mosque for the final ten days of Ramadan. This worship is called itikaf (retreat). They observe fast during the day and occupy themselves with the remembrance of God, performing voluntary prayers and studying the Qur'an, 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, thus they may not leave the precincts of the mosque except for a genuine religious purpose. Devoting time to remember God, Muslims hope to receive divine favors and blessings connected with the blessed night.
Prophet Muhammad was very particular in these regards. It is related that when the last ten days of Ramadan began, he used to keep awake the whole night and was most diligent in worship.
All Muslims believe that the incident occurred during the last third of the month of Ramadan but they differ as to the exact date. Sunnis generally consider it to be either the 21st, 23rd, 25th, 27th, or 29th  of the month; while Shi'as consider it to be either the 19th, 21st or 23rd of the month. Shi'as believe the 23rd to be the most important and 19th the least of the three. Conventionally, most Sunnis celebrate it throughout the night of the 27th (i.e. the night between the 26th and 27th). However, due to the uncertainty of the exact date, Muslims are recommended to observe all the nights as a matter of precaution.
Differences in lexicography
Although the literal translation of the word "Qadr" is "measure", the day has been popularly referred to as Night of Power. The proper way to translate "Laylat al-Qadr" has led to some controversy, some Muslims claiming that "Night of Power" is a mistranslation in Abdullah Yusuf Ali translation that got popular.
The term "Night of Power" comes from The Holy Qur'an: Text, Translation and Commentary by Abdullah Yusuf Ali (died 1953) who translated surat Al-Qadr verse one as:
We have indeed revealed this (Message) in the Night of Power:
Marmaduke Pickthall translates it as:
Lo! We revealed it on the Night of Predestination.
And Muhammad Asad writes:
Behold, from on high have We bestowed this [divine writ] on the Night of Destiny.
In the corresponding note he adds, "Laylatil-Qadr" can also be translated as "the Night of Almightiness" or "the Night of Majesty"