Tarawih prayer is a sunnah prayer that is done at night, in the month of Ramadan to be precise. The law is sunnah muakkad
The tarawih prayer has a very large virtue or fadhilah. Whoever does it in congregation, then the reward is calculated as one full night's prayer.
In the Durratun Nashihin book, it is explained in full about the virtues of tarawih prayers every night, throughout the month of Ramadan.