What does Hebrews 7:14 mean?

The Law of Moses did not provide for members of the tribe of Judah to become priests; this was reserved only for the descendants of Levi (Deuteronomy 18:1; Hebrews 7:5). Judah was the tribe of the king, after David (Genesis 49:10). For this reason, the nation of Israel experienced an irreconcilable split between the altar and the throne: no one could hold both offices at the same time. Long prior to Israel, however, Abraham encountered a man referred to as both priest and king: Melchizedek (Genesis 14:14–24).

This mysterious figure becomes an important part of the book of Hebrews. In these verses, the author is showing how Melchizedek foreshadowed the ministry of Jesus Christ. Clearly, God did not intend the Levitical priests to be our ultimate salvation, else He would not have promised to establish some other order "forever" (Psalm 110:4; Hebrews 7:11). Melchizedek is said not to have genealogy, symbolically describing him as without beginning or end, and his priesthood having the same quality (Hebrews 7:3).

This verse begins to tie some of these threads together: Jesus Christ is both priest and king (Hebrews 1:8–9; 5:5–6), just as Melchizedek was both priest and king (Genesis 14:18). Jesus is superior to Abraham (John 8:53–58), just as Melchizedek was greater than Abraham (Hebrews 7:6–7). The priesthood of Christ is superior to that of Levi and Aaron, since it was decreed by God, not by family line, in the same way Melchizedek's priesthood is beyond a family connection (Hebrews 7:20–21). This will all be wound together to show how Jesus Christ is exactly the fulfillment God has always intended for our salvation.