A supplication made during the middle of the last part of the night and after the conclusion of the obligatory prayers

رياض الصالحين بالعربية والإنجليزية - (ج 1 / ص 1901)
1500 - وعن أبي أمامة رضي الله عنه قال : قيل لرسول الله صلى الله عليه و سلم : أي الدعاء أسمع ؟ قال : [ جوف الليل الآخر ودبر الصلوات المكتوبات ] رواه الترمذي وقال حديث حسن
1500.

Abu Umamah (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) was asked: "At what time does the supplication find the greatest response?'' He (PBUH) replied, "A supplication made during the middle of the last part of the night and after the conclusion of the obligatory prayers.''

[At-Tirmidhi].

Commentary:

"Al-'Akhir'' is the characteristic of "Jauf'' and in the present context it means the late hours of night. "Jauf'' can also mean here "middle'', that is in the later-half of the night.

In other words, if the night is divided between two equal parts then it (Jauf) would be the middle of the second part. In either case it is the time of the night which in other Ahadith has been termed as the third part of the night. It is the time when Almighty Allah comes to descend on the sky of this world.
Prayers are also granted by Allah after the obligatory Salat.