The author retells the story of Genesis 14. Melchizedek, king of Salem and priest of God Most High, met Abraham as he returned from defeating the kings, blessed him, and Abraham gave him a tenth of everything. His name means king of righteousness, and king of Salem means king of peace. Scripture records for him no father, mother or genealogy, and no beginning or end of days; made like the Son of God, he remains a priest forever.
His greatness is clear: Abraham paid him a tenth, and Levi in a sense paid it through his ancestor. But if perfection had been attainable through the Levitical priesthood, what further need would there be for another priest to arise in the order of Melchizedek rather than Aaron? With a change in the priesthood there must be a change in the law. Jesus belongs to the tribe of Judah, from which no one has served at the altar, and has become a priest not by a legal requirement of ancestry but by the power of an indestructible life.
He is also a priest by oath: the Levites became priests without an oath, but Jesus with an oath from the Lord, who will not change his mind: You are a priest forever. This makes Jesus the guarantor of a better covenant. The Levitical priests were many because death prevented them from continuing; Jesus holds his priesthood permanently, and so he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.
The chapter ends with the high priest we needed: holy, innocent, unstained, separated from sinners and exalted above the heavens. He has no need to offer sacrifices daily, first for his own sins and then for those of the people, because he did this once for all when he offered up himself. The law appoints men in weakness as high priests, but the oath, which came after the law, appoints a Son who has been made perfect forever.