Everything concerning Traweeeh prayers

Abu Hurayrah narrated that the Messenger of Allah said, "Whoever establishes prayers during the nights of Ramadan faithfully out of sincere faith and hoping to attain Allah's rewards (not for showing off), all his past sins will be forgiven."
Tarawih Prayer is a special Prayer Muslims perform only in the month of Ramadan. It is a sunnah of the Prophet (peace and blessings be upon him), which means that it was his practice to perform Tarawih and Muslims are encouraged to do likewise, but it is not obligatory.

Tarawih is performed after `Isha’ (Night) Prayer. It can be performed at home, alone or in congregation, or at a mosque. In many mosques, one juz’ (30th part) of the Qur’an is recited each night in Tarawih. Thus performing Tarawih in the mosque imparts a special flavor to Ramadan, especially if one is able to do so every night and hear the whole Qur’an recited during the month.

Note that the Islamic day begins at sunset. Thus the first Tarawih Prayer of Ramadan will be performed the evening before the fast actually begins. Likewise, after the fast on the 29th day of Ramadan, the Tarawih Prayer is delayed until it is determined whether the new moon has been sighted, marking the end of Ramadan, or whether there will be one more day of fasting. If the new moon is sighted, there is no Tarawih Prayer.