... His strategy is comprehensive. He will show that Jesus was a superior priest in a superior sanctuary, with a superior sacrifice.
First, in Hebrews 7, the author of Hebrews shows how Jesus might be considered a priest. By the normal Old Testament criteria, Jesus would not be a priest in Israel, on earth (cf. Heb. 8:4). The Old Testament appoints the descendants of Levi, one of the sons of Jacob in Genesis, as those who would be priests for Israel. But Jesus' human family tree did not descend from Levi. Instead, he was from the tribe of Judah, the tribe from which the kings came (e.g., Heb. 7:14).
Hebrews would not have to argue that Jesus was a priest. Christians before the author of Hebrews, like Paul, used the metaphor of Jesus' death as a sacrifice without explicitly arguing that Jesus was a priest. In 1 Corinthians 5:7, Paul compares Jesus to a Passover lamb. In Romans 8:3, Paul compares Jesus' death to a sin offering. This same picture probably stands behind 2 Corinthians 5:21, where Paul says that God made Jesus to "be sin" for us.
To think of Jesus as a priest takes this metaphor of Jesus as a sacrifice to the next level.  Jesus becomes both the offering and the one offering. The closest Paul comes to calling Jesus a priest is when he says that the Christ who died now sits at God's right hand to intercede for us (Rom. 8:35).
But the author of Hebrews is making a comprehensive argument that the sacrificial system has been completely replaced. It serves this argument to show a sense in which Jesus might be a superior priest in a superior sanctuary with a superior sacrifice. Psalm 110:4 serves the author well to create this picture, since the earliest Christians could easily read this verse in relation to Christ.
Christians from the earliest days read Psalm 110:1 in relation to Jesus' resurrection. "The LORD says to my Lord: 'Sit at my right hand until I make your enemies a footstool for your feet'" (cf. Heb. 1:13) The earliest Christians heard this verse as a prediction that God would install the risen Messiah Jesus as king of the world at his right hand in heaven. It was thus easy for the author of Hebrews to go on and draw attention to verse 4: "You are a priest forever, in the order of Melchizedek" (e.g., Heb. 5:6).
So the Messiah would be a priest like Melchizedek. But who was Melchizedek and what was a priest in the order of Melchizedek? The answer to this question was to be found in Genesis 14, the only other place in the Old Testament where Melchizedek is mentioned.
In Abraham's day, Melchizedek was the king of a city called Salem. Tradition says that this city later became Jerusalem. He was also a priest of the Most High God at that time. So a priest in the order of Melchizedek, Hebrews argues, is a king-priest. The fact that Jesus is a king thus does not necessarily mean he cannot be a priest, because a priest like Melchizedek is both king and priest.
Also important for the author of Hebrews is the fact that Melchizedek was not priest because he came from a priestly lineage. As a priest, Melchizedek was "without father or mother, without genealogy" (7:3). In other words, he was not from a priestly line. He was not a priest "on the basis of a regulation as to his ancestry" (7:16). Genesis says nothing about when Melchizedek began to serve as priest, and it says nothing about when he died. In that sense, a priest like Melchizedek has no "beginning of days or end of life" (7:3).
For Jesus, this description was especially true, because God raised him from the dead. Indeed, this is the key to why Jesus' sacrifice is so effective. It was the sacrifice of an "indestructible life" (7:16). Other priests die. Jesus lives to serve as priest forever in a permanent priesthood (7:23-24).
And while the priests who descended from Levi were important, the author points out that Abraham gave tithes to Melchizedek, and Melchizedek blessed Abraham, not the other way around. This fact implies that Melchizedek was superior to Abraham. But if Melchizedek is greater than Abraham, and Levi is a descendant of Abraham, then king-priests like Melchizedek must be superior to earthly priests who have descended from Levi. 
So the author has powerfully argued that Jesus is a superior priest to any earthly priest. Next he will argue that Jesus offered his sacrifice in a superior sanctuary to any earthly sanctuary...
 A metaphor is when you create a new meaning by comparing two unlike things (cf. P. Ricoeur, The Rule of Metaphor: Multi-Disciplinary Studies in the Creation of Meaning in Language [London: Routledge, 1978]). So a literal sacrifice involved killing an animal as an offering to a god. That was not the normal, literal sense of what a crucifixion was at the time of Christ. To compare Jesus' death to a sacrifice was thus a metaphorical way of thinking of it.
 There has only been one priest after the order of Melchizedek in all of history. Many have suggested in the past that Melchizedek himself may have been Christ come to earth. But since Hebrews never says this idea, I think it is more likely that Hebrews is really interested in Psalm 110:4 and what a priest of the order of Melchizedek would be like. To find out, the author draws on the description of Melchizedek in Genesis 14.
But the author is not ultimately interested in the Melchizedek of history. Using some of the tools of Jewish interpretation at the time, he uses the story of Melchizedek in Genesis to discover what such a priest would be like. But, ironically, not even Melchizedek himself was such a priest. Only Jesus.