Melchizedek is a character in Genesis. What's odd in Genesis is after the fall of Adam, every single main character has a small genealogy. Noah had so many children, lived so many years, and he died. The next person lived so many years, had so many children and he died. The next person lived so many years, had so many children, and he died, and he died, and he died, and he died.
The author of Hebrews picks up this character called Melchizedek, and one of the first things he states is, "This person has no record of either birth or death." Now is Melchizedek a theophany? I think the answer to that is no. And I think we know that because the people in the story of Genesis 13 and 14 recognize Melchizedek as a person, so this is a real king who lived in a real time who had a real kingdom.
Now what's interesting about Melchizedek, one, there is no record of his birth or his death. It doesn't mean he's eternal, it just means in a book of Genesis, which is a genealogical book, does not give the record. Secondly, his name: Melchizedek." Melek Zedek." "Melek" in Hebrew means "king." "Zedek" in Hebrew means "righteousness." He's a king of righteousness. Furthermore, we need to look at his kingdom. He's the king of Salem, and in Hebrew that root word is "Shalom" or "peace." He's the king of righteousness whose kingdom is a kingdom of peace.
The book of Hebrews then points to Melchizedek as a type of Christ, in that Jesus Christ is a priest, not of the Levitical order. He does not do his work inside the earthly tabernacle, but He does it in the heavenly realities. Why? He's a priest of a different order, an eternal order, one that has no beginning or no end. Thus, the genealogical factor.
Second of all, Jesus Christ in his death, conquers sin and death itself. Thus, He is the king who has conquered sin and death and brought peace to his kingdom. And He's also the great high priest who sits right now at the right hand of God the Father, making priestly intercession on our behalf. So Melchizedek is a type of Christ. Christ is the fulfillment of Melchizedek in that he is the great high priest who has ushered in the rule of peace. That's why the book of Revelations says, "In heaven there will be no more tears, no more wailing, no more covenant curses because our king who has given us righteousness, Melek Zedek, has also given us a reign of covenant blessing, no more tear, no more sorrow.