The order of Melchizedek is the earliest priesthood mentioned in the Bible, with Melchizedek as the first priest mentioned by name in the Holy Scripture. Psalm 110 of the King James Bible identifies the order of Melchizedek as being the line through which Israel's Davidic king is later ordained.
Jesus Christ, after resurrection, is described as a priest forever of the order of Melchizedek, effectively drawing a line from the very first priest in Biblical history to the resurrected Son. The writer of the Book of Hebrews distinguishes Jesus as a priest in the order of Melchizedek because Jesus, not being a descendant of Aaron, is not qualified for Jewish priesthood according to the Law of Moses. Melchizedek himself is a priest-king whose name means "King of Righteousness". He appears in the Book of Genesis.
In Roman Catholic tradition, priests are ordained to the order of Melchizedek, forming a continuity with the beginning of Abram's journey into the faith, when Abram presents Melchizedek with a tithe and receives a blessing from the priest-king in return. The Epistle to the Hebrews in the New Testament considers that this makes the order of Melchizedek superior to the priesthood of Aaron. Aaron, being in the loins of Abraham at the time of his blessing, could not be greater than Melchizedek, the one who performed the blessing.