Sometimes, New Testament writers place new meanings on Old Testament texts. Isaiah 7 speaks of a young woman giving birth to a child, but the New Testament gives another meaning: the young woman is a virgin. Both meanings are correct in their respective contexts. But sometimes, Old Testament passages are given a specific New Testament meaning and the Old Testament passage could not have meant anything else.
This is the case with Psalm 110. It is cited or alluded to eighteen times in the New Testament and all of the uses refer to Jesus.
Psalm 110 says it was written about David. At first glance, it appears to be a general prayer for the king, but closer examination reveals it is more than that. David, the king, speaks of his Lord who sits at the right hand of God. Additionally, this lord/king is also a priest in the Melchizedek order. And yet, in the Old Testament, kings were not priests, and there is nothing about the Melchizedek order in the Old Testament.
The easiest explanation of the Psalm is that God has revealed to David something of Jesus, and David has passed it along in this Psalm, exalting the coming of an unstoppable king who also serves as a priest. This is the interpretation Jesus places on it in Matthew 22:44, an interpretation seemingly accepted by Jewish leaders in his own day.
What did David know about Jesus? Probably not what we know, but God had revealed something of him to David. Interesting, is it not, the notion that the coming of Jesus was such a wonderful treat in the mind of God that here and there in the Old Testament, He gives us glimpses into Christ’s coming.