All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Taraweeh prayer in Ramadan is a confirmed Sunnah. Abu Hurayrah said: “The Prophet used to urge the people to pray night prayers in Ramadan without him authoritatively ordering them to do so.” The Prophet said: “Whoever stands at night prayer in Ramadan while believing in Allah Who prescribed it and while seeking its reward from Him, will have his past sins forgiven.” [Muslim]
Besides, ‘Aa’ishah narrated that once the Prophet prayed (the night prayer) in the mosque and some people prayed behind him, then he prayed the second day, and many people prayed behind him, then the people gathered to pray with him the third or fourth night, and the Prophet did not go out to pray with them. In the morning, the Prophet told them: ''I know what you did [gathering for the prayer] and nothing prevented me from coming out to you except that I feared that it would become an obligation on you.”; and this was during Ramadan.” [Al-Bukhari and Muslim]
To conclude, Taraweeh prayer is not an obligation; rather, it is a confirmed Sunnah. Nonetheless, a Muslim should not prevent himself from the virtues of standing at night prayer in Ramadan on the pretext that it is a Sunnah and not an obligation [Waajib], as a believer should be keen on doing good and performing acts of obedience to Allah especially during the reasons of righteousness which cannot be replaced.
Allah knows best.