In Alma 13:18 it says that:
"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."
According to John Welch, Melchizedek was a man of God and peace because he had obtained the spiritual powers and knowledge necessary to lead his people into the rest of the Lord through the order of the Son. . . .
Although Alma's discourse contains a noteworthy use of the material about Melchizedek in Genesis 14:17-24, Alma's text is of particular interest because it is unique--sui generis. No other known sermon has imputed such a practical religious and ceremonial meaning to Melchizedek, although in certain respects the sacerdotal approach of 2 Enoch and the account in the Joseph Smith Translation come close. . . .
Alma's sermon in chapters 12 and 13 teaches the principle that God will provide man access to certain mysteries of God (Alma 12:9-11). . . . Alma says that many know these mysteries as priests (Alma 13:1), but they are laid under a strict condition of secrecy (Alma 12:9) that can be lifted only by the diligence and repentance of the children of men (Alma 12:9-11; 13:18; cf. Alma 26:22). [John W. Welch, The Melchizedek Material in Alma 13:13-19," in By Study and Also by Faith, Vol. 2, pp. 238-240]
According to Robert Millet, Josephus explained that the city of Salem, over which Melchizedek reigned, later became known as Jerusalem ("The Antiquities" 1.10.3.). In writing of Jerusalem, Josephus observed: "He who first built it was a potent man among the Canaanites and is in our tongue called [Melchizedek] the Righteous King, for such he really was; on which account he was [there] the first priest of God, and first built a temple [there], and called the city Jerusalem, which was formerly called Salem." ("The Wars" 6.10.1; emphasis added). And most important for our study, the legends attest that Melchizedek was both king and priest in Salem (Hebrews 7:1; Ginzberg 1:233). [Robert L. Millet, "The Holy Order of God," in The Book of Mormon: Alma, The Testimony of The Word, pp. 79-80]
Note* Thus, this "office of the high priesthood according to the holy order of God" which Melchizedek received (Alma 13:18) apparently had something to do with the mysteries of God, secrecy, temples, preaching the gospel of repentance, establishing peace, and becoming a king and a priest. To Latter-day Saints, the significance of these items can be found in priesthood and temple covenants. This is another clear reminder that the purpose of the Book of Mormon is to "show unto the remnant of the House of Israel what great things the Lord hath done for their fathers . . . that they may know the covenants of the Lord . . ." (Preface) [Alan C. Miner, Personal Notes]