This Hadith tells us that the Prophet (PBUH) was in the habit of lying down on his right side after the two Sunnah of Fajr prayer. It also mentions his offering of Tahajjud prayer, which consists of eleven Rak'ah. He would perform this Salat in the form of four couplets and one Witr. According to some narrations, he would perform four couplets and supplement them with three Rak'ah of Witr. Both these forms are right. This Hadith, also proves the validity of one Witr.
This Hadith also tells us that the time for the Tahajjud and Witr prayer is from 'Isha' prayer to the daybreak. One can perform Tahajjud prayer at any time during this period. But, the best time for it is the third part of the night for the reason that after Tahajjud one can, after a while, perform Fajr prayer in congregation (Jama'ah).
The Tarawih (optional night prayer) performed in the month of Ramadan is this Tahajjud prayer which is also termed as Qiyam-ul-Lail For the sake of convenience and benefit of congregational prayer, it is offered soon after 'Isha' prayer in the month of Ramadan. The right number of Rak'ah in the Tarawih prayer is eight because the Prophet (PBUH) never offered more than eight Rak'ah; with three Witr in the month of Ramadan or otherwise. 'Aishah's statement to this effect quoted in Sahih Al-Bukhari also supports this fact. In Hadith literature, the Nawafil of the night have been termed as Qiyam-ul-Lail for which the word "Tahajjud" has also been used in the Qur'an and Hadith. The word "Tarawih" does not figure anywhere in Hadith. The word "Tarawih" for "Qiyam-ul-Lail" became popular after the era of the Prophet (PBUH) and his Companions. Thus, that number of Tarawih prayer agrees with the Sunnah of the Prophet (PBUH) which is proved by the actual practice of the Prophet (PBUH), that is eight Rak'ah and three Witr only. It is not in any case twenty Rak'ah. Authentic Ahadith prove this point abundantly.