"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.