For this Melchizedek, king of Salem, priest of the Most High God, met Abraham returning from the slaughter of the kings and blessed him, and to him Abraham apportioned a tenth part of everything. He is first, by translation of his name, king of righteousness, and then he is also king of Salem, that is, king of peace. He is without father or mother or genealogy, having neither beginning of days nor end of life, but resembling the Son of God he continues a priest forever.
See how great this man was to whom Abraham the patriarch gave a tenth of the spoils! And those descendants of Levi who receive the priestly office have a commandment in the law to take tithes from the people, that is, from their brothers, though these also are descended from Abraham. But this man who does not have his descent from them received tithes from Abraham and blessed him who had the promises. It is beyond dispute that the inferior is blessed by the superior. In the one case tithes are received by mortal men, but in the other case, by one of whom it is testified that he lives. One might even say that Levi himself, who receives tithes, paid tithes through Abraham, for he was still in the loins of his ancestor when Melchizedek met him. (Hebrews 7:1-10, ESV)
The author of Hebrews goes on from elementary doctrines to an exposition of this strange figure Abraham meets upon his march home after victoriously defeating the kings who captured his nephew Lot and the cities of Sodom and Gomorrah. Melchi means ‘my king’ and zedek means ‘righteous’ and this priestly king comes from Salem (means ‘peace’) the original name for Jerusalem. No account is given of his genealogy or death so it is as if he lives forever (though he was just a man and did in fact have a birth and a death). He thus resembles the Son of God, Jesus, as a priest forever.
Abraham shows deference to Melchizedek by paying him a tenth of the spoils of the war. And because Levi comes from Abraham and is inferior to him in that way, Levi, in essence, paid tithes and deference to this priest.
The readers should be getting the idea that the priesthood and ritual they want to return to in the religion they followed as Jews before they became followers of Jesus is in fact inferior to the priesthood of Jesus. He is a priest forever after the order of Melchizedek, unlike Aaron from the tribe of Levi.
Don’t you see that what you were saved from is and always will be only a feeble whisper of what God has shouted to us in Christ. We were making our own way in life without realizing that God had something better all along. But we wanted to do it our way. We couldn’t trust God to lead us, or so we thought. Then He broke through our hardness of heart and rescued us. Why would we ever give that up?