Who is Melchizedek in the Bible? Some argue he is the preincarnate Christ, others believe the Hebrews author is speaking figuratively. If he wasn't Jesus, then how did he rank spiritually higher than Abraham to the point of Abraham giving him tithes?
"Therefore, if perfection were through the Levitical priesthood (for under it the people received the law), what further need was there that another priest should rise according to the order of Melchizedek, and not be called according to the order of Aaron? For the priesthood being changed, of necessity there is also a change of the law. For He of whom these things are spoken belongs to another tribe, from which no man has officiated at the altar. For it is evident that our Lord arose from Judah, of which tribe Moses spoke nothing concerning priesthood. And it is yet far more evident if, in the likeness of Melchizedek, there arises another priest who has come, not according to the law of a fleshly commandment, but according to the power of an endless life. For He testifies: "You are a priest forever according to the order of Melchizedek"" (Hebrews 7:11-17).
The author of Hebrews is not stating that Jesus was Melchizedek, but that Jesus had attributes similar to Melchizedek ("in the likeness of").
Melchizedek was the king of a city-state called Salem, he also was a priest of the one true God (Genesis 14:18). This stands out because it shows that the worship of God was not limited to Abraham's lineage. Jesus also is both our King and our High Priest. The author of Hebrews quotes Psalms 110:4 to prove this was always a part of God's plan. The Messiah would not only be a king, but also a priest. It was long prophesied that the Messiah would be of the tribe of Judah and of the lineage of David, but the priests came from the tribe of Levi and of the linage of Aaron. For the Messiah to be both king and priest, the law that separated these two positions would have to change.
There are other ways that Jesus and Melchizedek are similar. "For this Melchizedek, king of Salem, priest of the Most High God, who met Abraham as he was returning from the slaughter of the kings and blessed him, to whom also Abraham apportioned a tenth part of all the spoils, was first of all, by the translation of his name, king of righteousness, and then also king of Salem, which is king of peace. Without father, without mother, without genealogy, having neither beginning of days nor end of life, but made like the Son of God, he remains a priest perpetually" (Hebrews 7:1-3). Melchizedek means "king of righteousness" which is also an appropriate title for Jesus.
Melchizedek was also king of Salem, and "Salem" means "peace." Jesus, too, can be described as the king of peace. In addition, Melchizedek is a bit of a mystery. He appears in Genesis without any mention of who his father was or where he came from. Nor are we ever told what became of Melchizedek. That unfinished story leaves us hanging. While people knew who Jesus' earthly parents were, they didn't know the whole story. Jesus pre-existed his time on earth. He lives eternally, which always puzzles people in how to describe the eternal Jesus as the Son of the Eternal Father. Eternity implies no beginning or end -- sort of like the story of Melchizedek, though logically we know that Melchizedek did have a beginning and an end. However, the Hebrews writer argues that we can say that Melchizedek's priesthood continues since we are not told it ended.
Abraham gave Melchizedek a tenth of the spoils from his battle with the kings from Elam and the neighboring counties because Melchizedek was a priest of God. This was a way for Abraham to thank God for his success.
"Now observe how great this man was to whom Abraham, the patriarch, gave a tenth of the choicest spoils. And those indeed of the sons of Levi who receive the priest's office have commandment in the Law to collect a tenth from the people, that is, from their brethren, although these are descended from Abraham. But the one whose genealogy is not traced from them collected a tenth from Abraham and blessed the one who had the promises. But without any dispute the lesser is blessed by the greater. In this case mortal men receive tithes, but in that case one receives them, of whom it is witnessed that he lives on. And, so to speak, through Abraham even Levi, who received tithes, paid tithes, for he was still in the loins of his father when Melchizedek met him" (Hebrews 7:4-10).
The author of Hebrews point is that Abraham gave a tenth to someone and received a blessing from the same person. Typically it is the greater person who blesses the lesser person. This then means Abraham saw Melchizedek as a greater person than himself, despite the promises Abraham had from God. This logically means that Abraham's descendants, who are beneath Abraham, though at this time unborn, are also beneath Melchizedek. The Levites, in particular, collect a tithe, but that tithe only comes from their own brethren. Melchizedek received a tithe from an unrelated person, so again he is the greater.
All of this is mentioned to provide evidence that the priesthood of Melchizedek is greater than the priesthood of Aaron. Thus, Jesus being a priest after the order of Melchizedek is a part of a greater order of priests.