Melchizedek, King of Salem, is a person in the Bible with fascinating significance. Melchizedek first appears in Genesis 14. After Abram won several battles, Melchizedek gives bread and wine to Abram, and blesses him. Abram then gives Melchizedek a tenth (a tithe) of everything.
Later on in Psalm 110, a Davidic Psalm which also declares the ultimate victory of Messiah, the Scripture tells us that God’s son is “a priest forever in the order of Melchizedek.” At first glance it may seem odd to use the language “a priest forever in the order of Melchizedek,” since the Old Testament priesthood was not explained until Moses and Aaron’s day, well after Melchizedek. (Exodus 28)
The key to understanding who Melchizedek is lies in recognizing that Melchizedek is a prefiguring of the ministry of Jesus Christ. Melchizedek was a real person, not an angel or simply an appearance of God. A “type” in biblical theology is a person or event which fulfills a certain role in a particular time period, which is then later fulfilled completely in Jesus Christ. A familiar example is this: The prophet Jonah is a “type” with respect to the resurrection of Jesus. Jonah spent time in the belly of the great fish, and he was spit onto dry land and survived. In a similar way, Jesus died and was buried in the tomb before rising again. A “type” in the Old Testament is later fulfilled in the New Testament by what is called an “antitype.”
Melchizedek is a type, or a pattern, of the true high priest- Jesus-who would come later. Melchizedek is a precursor to the ministry of Jesus Christ as High Priest in two ways: his name- “King of Righteousness”, and the fact that Melchizedek does not have a recorded ancestors or descendants.
The book of Hebrews explains this significance, and it emphasizes that the ministry of Jesus was even greater than Melchizedek.
 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. (Hebrews 7:1-3 ESV)
Melchizedek resembles Jesus Christ, because Melchizedek does not have recorded ancestors or descendants, a hint of eternality. Melchizedek was also outside the line of the Aaronic priesthood, determined by birth. These facts about Melchizedek’s life point forward to the ministry of Jesus Christ. Jesus was outside the line of Aaron, and Jesus exists eternally along with the Father and the Spirit. Jesus’ priesthood last forever because He has risen and he will never die.
 This becomes even more evident when another priest arises in the likeness of Melchizedek,  who has become a priest, not on the basis of a legal requirement concerning bodily descent, but by the power of an indestructible life. Hebrews 7:15–16 ESV
The author of Hebrews is bringing out the contrast between Melchizedek and the priests descended from Aaron- the Levitical priests. In drawing the similarity between Melchizedek and Jesus, the author is showing the superiority of Jesus’ priesthood to that of any human priest, even Melchizedek included. The climax of this contrast between Jesus our great High Priest and the earthly priests is brought out at the end of Hebrews chapter 7:
 This makes Jesus the guarantor of a better covenant.  The former priests were many in number, because they were prevented by death from continuing in office,  but he holds his priesthood permanently, because he continues forever.  Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.  For it was indeed fitting that we should have such a high priest, holy, innocent, unstained, separated from sinners, and exalted above the heavens.  He has no need, like those high priests, to offer sacrifices daily, first for his own sins and then for those of the people, since he did this once for all when he offered up himself. (Hebrews 7:22-27 ESV)