As Alma the younger is preaching to the people in Ammonihah, he takes some time to tell them about priesthood authority and also about Melchizedek.
17 Now this Melchizedek was a king over the land of Salem; and his people had waxed strong in iniquity and abomination; yea, they had all gone astray; they were full of all manner of wickedness;
18 But Melchizedek having exercised mighty faith, and received the office of the high priesthood according to the holy order of God, did preach repentance unto his people. And behold, they did repent; and Melchizedek did establish peace in the land in his days; therefore he was called the prince of peace, for he was the king of Salem; and he did reign under his father.
19 Now, there were many before him, and also there were many afterwards, but none were greater; therefore, of him they have more particularly made mention. (Alma 13:17-19)
This account is more than is in the Bible (excepting the JST about Melchizedek), but it still seems rather bald, and we have to read between the lines a bit.
Melchizedek was king over Salem, and his people were very wicked. This must have been very distressing to Melchizedek. But he could do something about it. After all, he was king. And he had choices about what he could do. He could either enforce the law and punish all his people, or he could preach repentance to them and hope they would listen.
He chose to preach repentance. So he received the high priesthood and he preached… and happily, his people chose to repent! (Yaaaaay! Celebrations all around!) And because they repented, the city was much more peaceful and the people all had peace in their lives, and things were so much better after that.
So why did Alma tell this to the people of Ammonihah? I think he hoped they would realize that Alma himself was essentially trying to do the same thing Melchizedek did—preach repentance to the people instead of going out and enforcing the law immediately. He had given up the chief judge position specifically so he could do that. He hoped the people would take the hint and humble themselves and repent.
It hit me that Melchizedek was also a type of Christ. Christ is the king over the earth, and He sees that all His people are wicked, and He could just enforce justice, but He wants to save His people. So he, as high priest forever, walked among them and preached repentance (and he sends others to preach repentance as well). (So I guess Alma, in emulating Melchizedek, also is a type of Christ.)
Another way Melchizedek was a type of Christ was in how it was said he was king over Salem and he reigned under his father. Melchizedek was a prince who was also king, but he was a client king under his father. In the same way, Christ is king, but He also reigns under Heavenly Father.
Coolness! I love finding types of Christ I haven’t seen before!