The writer of Hebrews has a big problem. He needs to show how Jesus is our great high priest; however, everyone in his audience would know that high priests come only from the tribe of Levi. He finds a solution to this problem in Psa 110.4:
The LORD has sworn and will not change his mind: “You are a priest forever, in the order of Melchizedek.”
This psalm originally celebrated God’s support of the king of Israel while also noting the king’s priestly role (see 1 Chr 15.27 where King David does priestly things). Furthermore, this psalm connects the king’s priesthood with another kind of priest, the mysterious Melchizedek.
Outside of Hebrews and Psa 110, the only other reference to Melchizedek is Genesis 14.18-20.
Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High,
and he blessed Abram, saying,
“Blessed be Abram by God Most High,
Creator of heaven and earth.
And blessed be God Most High,
who delivered your enemies into your hand.”
Then Abram gave him a tenth of everything. (Genesis 14.18–20 NIV)
Three verses—that’s it. And those three verses are plopped in the middle of a story about how Abraham defeated five tribal chiefs to rescue his nephew Lot. Thus, just as these verses seem to come out of nowhere, so does Melchizedek.
Melchizedek (whose name is King + Righteousness in Hebrew) the king of Salem (the word for Peace) is a priest of El Elyon (God Most High) who for no reason mentioned blesses Abraham. After the blessing, Abraham gives Melchizedek a tenth of his spoils from the tribal chiefs. Then, just as suddenly, Melchizedek disappears from the Bible until Psa 110.
The preacher of Hebrews follows this logic: Since Jesus is not of the tribe of Levi he should not be able to be a priest of any kind. However, the priest Melchizedek predates the Levitical priesthood. That he blessed Abraham, the great-grandfather of Levi, shows that Melchizedek is greater than Abraham who further confirms this by giving a tenth to Melchizedek. In this way, Levi—who has not been born yet—gave a tenth to Melchizedek. Therefore, Melchizedek is greater than Levi. Consequently the Melchizedekian priesthood is greater than the Levitical priesthood.
Ok, it may not be our logic, but you can still follow it.
The point: Jesus’ priesthood is superior to that of the tribe of Levi.