I found a quick and concise article on the internet that explains the title “Ancient of Days”. It is found on gotquestions.com, a christian website.
The title “Ancient of Days” first appears inDaniel 7:9, where Daniel is describing his vision of heaven. There an ancient, or venerable, Person sits on a flaming throne with wheels of fire, His hair and clothing white as snow. The flaming throne is symbolic of judgment, while the white hair and title “Ancient” indicate that God existed before time began. InIsaiah 43:13, we find that God refers to Himself existing from ancient of days (literally, “before days were”). That means God existed before days were even created. We read in Genesis 1 that God created time, days and nights, so God existed from before the beginning of time. God is often represented as ancient, as He that is “from everlasting to everlasting” (Psalm 90:2) and as “the first and the last” inIsaiah 44:6.
There can also be no doubt that the reference in Daniel 7 is to God as Judge. A similar description occurs inRevelation 1:14-15, wherein Christ is described as having snow-white hair and blazing eyes. In Revelation, God the Son is depicted with the same power of judgment over His church as the Ancient of Days is described as having in judging Israel. In fact, His sharp gaze judges all seven of the churches in Revelation 1–3 with complete clarity of the reality of all there is to know.
The title “Ancient of Days” is found only three times in Scripture, all three in prophetic passages inDaniel 7:9,13, and22. Verse 22 refers specifically to Jesus whose judgment will be part of the end-times events. InDaniel 7:13, the term “ancient of days” refers to God the Father, and we see Him on His throne as Jesus, the “Son of Man” approaches the throne on clouds. God is a triune God, meaning three Persons in One, and at different times “Ancient of Days” refers to Jesus Christ and at other times, to God the Father. But in the prophetic sense, it clearly refers to Jesus, the Ancient of Days returning to pronounce judgment on the world (Daniel 7:22).