To stand for prayer late at night, when no human can see you, gives tranquility and serenity to the heart. In an authentic hadith, the Prophet (bpuh) said that waking up late at night, remembering Allah, making ablution, and then standing for prayer makes one active and joyful.
(They used to sleep but little by night [invoking their Lord and praying, with fear and hope].)
(Quran 51 : 17)
(And in some parts of the night [also] offer the prayer with it [i.e. recite the Qur'an in the prayer], as an additional prayer [Tahajjud: optional prayer]...) (Qur'an 17: 79)
An authentic hadith in Abu Dawood indicates that performing the late-night prayer removes sickness from the body. The Prophet (bpuh) said:
"Don't be like so and so. He used to stand at night (for prayer), and then he abandoned doing so."
The following is related in a narration from 'Abdullah ibn 'Umar (may Allah be pleased with him):
"Abdullah is a good man, but would that he stood at night (for prayer)."
Don't grieve over things that are fleeting: everything in this universe will perish except Allah.
Everything will perish save His Face. (Quran 28: 88)
(Whatsoever is on it [the earth] will perish. And the Face of your Lord full of Majesty and Honor will abide forever) (Qur'an 55: 26-27)