Why Melchizedek?

 When Alma and Amulek are preaching to the people of Ammonihah, Alma is explaining to Zeezrom the plan of redemption, starting with the fall of Adam (Alma 12). Then in the next chapter he seems to randomly launch into a discussion of the priesthood and how Melchizedek was a high priest after the order of the son of God (Alma 13).  What does Melchizedek have to do with the fall of Adam and the plan of redemption?

To answer that question, you have to remember a couple of things from the Old Testament. The story of the fall of Adam sets up the main conflict of the Old Testament.  Man is thrust out of the presence of God and cannot return without divine assistance. In the Old Testament that assistance comes with the establishment of temples and priesthood. In the First Temple Period, people are ritualistically cleansed through blood sacrifice and then the High Priest, acting as proxy for the whole nation, is admitted into a symbolic garden of Eden (i.e. Holy of Holies) and the presence of the Lord (before the Mercy Seat), thus overcoming spiritual death.

Of course, in the Old Testament, the only people who could be High Priests were direct descendants of Aaron. This was a problem for the Lehites when they left Jerusalem because they were descended from Manasseh, not Aaron. They built temples in the New World, but there was no one, according to the Jewish law, who could act as High Priest. It seems that they resolved that problem the same way that Paul resolved the problem of Jesus' claim to be a High Priest in the book of Hebrews chapter 7. I that chapter, Paul claims that Jesus' authority comes not through Aaron, but through an older priesthood, after the order of Melchizedek. (Hebrews 7:17) In Alma 13, Alma seems to be using the same kind of argument to justify ordaining High Priests, not according to Levitical law, but through the older Melchizedek priesthood.  These priests could establish and run temples, which showed the people how to overcome original sin, and return to God's presence.  

Of course, Alma was not ignorant of another good reason to bring up Melchizedek.  Melchizedek was a religious leader to was able to take a wicked people and lead them into righteousness. That is what Alma was trying to do with the people of Ammonihah. Melchizedek is a type of Christ.  His name means, "Righteous King" which is also a title of Jesus. Alma hopes that the people of Ammonihah will be encouraged and inspired by the story of Melchizedek as a type of Jesus, to repent and have hope for eternal life.