My intrigue of Psalm 110 led me to do some research on it. I was blown away with the depth of this Psalm that I didn't even begin to understand. As I have done before, I want to share the words from The New Bible Commentary on Psalm 110, as I think you might find the background pretty interesting, too.
The very name, Melchizedek, breathes an air of mystery. He enters Scripture unheralded. Abram has just conquered the kings of earth (Gn. 14:14–15) but when ‘Melchizedek king of Salem’ came, Abram acknowledges his pre-eminence as priest, presenting him with a tithe of the spoil (14:20) and affirming Melchizedek’s ‘God Most High’ to be none other than the Lord himself (14:22). In Joshua 10:1 we meet Adoni-Zedek. His name is identical in form and meaning (‘king of righteousness’) with Melchizedek, suggesting the continuation through the years of a priestly-kingship in Jerusalem. If so, when David took Jerusalem (2 Sa. 5:6–9) he sat on Melchizedek’s throne, himself heir to the priestly-kingship validated by Abraham. This would account for Psalm 110.
As David meditated on his dignity as priest-king, it became a telescope turned on the Messiah and he looked forward to the perfect Priest-King, the full reality of what David was only the shadow cast beforehand. When Hebrews (6:20–7:28) uses Melchizedek in order to show that the Lord Jesus is a true priest though without Aaronic ancestry, it is the fulfilment of a line of truth reaching back through David to Abraham. Jesus is indeed the true Melchizedek of whom Abram met the prototype, David was the foreshadowing and of whom Zechariah spoke.
The psalm consists of two parallel movements: the king (1–3) and the priest (4–7). Each begins with a divine promise, declares the status of its subject as king and priest, pledges his dominion, from Zion, over earth’s kings. It contrasts the willing devotion of his people with the overthrow of the nations and shows the King-Priest himself as ever-fresh with youthful vigour and ever-refreshed by timely renewal.