Hebrews 7 explains Psalm 110:4, You are a priest forever, after the order of Melchizedek. Genesis 14 says Melchizedek, king of Salem and priest of God Most High, blessed Abraham, and Abraham gave him a tenth. Hebrews draws out the meaning. His name means king of righteousness, and his city means peace. Scripture records no parents or genealogy for him, so he serves as a picture of a priest whose priesthood has no end. Since the lesser is blessed by the greater, Melchizedek ranks above Abraham, and in a sense above Levi, who was still in the body of his father when Melchizedek met him.
Verses 11 to 19 ask a question. If the Levitical priesthood made people perfect, why would God promise a different priest from another order? The answer is that the priesthood changed, so the law changed too. Jesus came from Judah, a tribe with no priests. He became a priest not after the law of a fleshly commandment, but after the power of an endless life. The law made nothing perfect, and God brought in a better hope, through which people draw near to God.
Verses 20 to 28 add two more contrasts. Levitical priests served without an oath, but God swore an oath about this priest. Many priests served because death kept stopping them, but he, because he lives forever, has his priesthood unchangeable. Therefore he is able to save to the uttermost those who draw near to God through him, since he lives forever to intercede. Holy, guiltless, and undefiled, he offered himself once for all.