There are many sources for this term, including:
I beheld till the thrones were cast down, and the Ancient of Days did sit, whose garment was white as snow, and the hair of his head like the pure wool: his throne was like the fiery flame, and his wheels as burning fire.
Whenever Judgment looms and the forehead of the Impatient One is revealed, the Forehead of the Ancient of Ancients is revealed; Judgment subsides and is not executed.This term appears three times in the book of Daniel (7:9, 13, 22), and is used in the sense of God being eternal.
Idra Rabba, Zohar 3:136b
The most powerful effect of this particular Name of God stems from the Jewish mystical book the Zohar, the seminal document of Kaballah that stems from 13th century Spain. In the Kaballah there is mention of the Ancient of Ancients, also interpreted as En Sof or the unmanifested God. The Ancient of Days is the manifestation of the Ancient of Ancients in space and time. The Kaballah goes into great detail describing the White Head of God and ultimately the emanation of its personality or attributes.
In Eastern Orthodox Christian hymns and icons, the Ancient of Days is most properly, in accordance with Orthodox theology, identified with God the Son, or Jesus Christ. As such, Eastern Christian art will sometimes portray Jesus Christ as an old man, the Ancient of Days, to show symbolically that he existed from all eternity, and sometimes as a young man to portray him as he was incarnate.
It was declared by the Russian Orthodox Church at the Great Synod of Moscow in 1667 that the Ancient of Days was the Son and not the Father against those that taught otherwise. In the Western Church similar figures usually represent only God the Father.
In the hymn "Immortal, Invisible, God only Wise", the last two lines of the first verse read:
Most blessed, most glorious, the Ancient of Days,Daniel 7:13-14 says, “I kept on beholding in the visions of the night, and, see there! with the clouds of the heavens someone like a son of man happened to be coming; and to the Ancient of Days he gained access, and they brought him up close even before that One. And to him there were given rulership and dignity and kingdom, that the peoples, national groups and languages should all serve even him. His rulership is an indefinitely lasting rulership that will not pass away, and his kingdom one that will not be brought to ruin."
Almighty, victorious, Thy great Name we praise.
In Buddhism, in the Kevattha Sutta (Digha Nikaya 11), the term "ancient of days" is referred to the creator God Brahma,
“I am the Great Brahma, the Supreme, the Mighty, the All-seeing, the Ruler, the Lord of all, the Controller, the Creator, the Chief of all, appointing to each his place, the Ancient of days, the Father of all that are and are to be.”The Sanskrit name for "Ancient of Days", Karttikeya or Skanda, is revered as one of the four (or seven) sons of Brahma in Hinduism.
In the Bahá’í Faith, 'the Ancient of Days' is one of the titles with which Bahá’u’lláh refers to himself.
In Esoteric tradition, the Ancient of Days is also known as Sanat Kumara.