From Hebrew Malki-tzedek — "My king is righteousness" (or "king of righteousness"). Melchizedek appears in Genesis 14 as the king of Salem (later Jeru-salem) and priest of God Most High, who blesses Abraham after the rescue of Lot and receives a tithe from him. He vanishes from the narrative as suddenly as he came. Psalm 110 — the most-quoted OT text in the NT — prophesies that the Davidic Messiah will be a priest "forever after the order of Melchizedek." Hebrews 7 interprets the order: priesthood older than Levi (Abraham was the great-grandfather of Levi; Melchizedek preceded them both); priesthood combining king and priest (forbidden under Aaron); priesthood untethered from genealogy and death.
The Melchizedek priesthood solves a problem Jewish readers of Hebrews faced: if Jesus is not from the tribe of Levi (He's from Judah), how can He be a priest at all? The answer: He's a priest in an older, higher order — one anticipated by Melchizedek centuries before Aaron was born. Hebrews 7:3 describes Melchizedek as "without father or mother or genealogy, having neither beginning of days nor end of life" — not a claim about Melchizedek's ontology, but about how he appears in the text (the Torah records no parents, no death, no successor — unusual for a priestly figure). He is a literary type of the eternal Son. Christ fulfills the order: King-Priest of the heavenly Salem, tithed by Abraham (in the person of his descendant Levi, Heb 7:9-10), priest by divine oath not by birth, priest forever because death cannot hold Him. Roman Catholic sacramental priesthood and LDS priesthood claims both misread this passage — the point of Hebrews is that Melchizedek's order is singular to Christ and non-transferable.