He was the King of Salem (Gen. 14:18) and a Priest of “G-d most high” (El elyon ) the first time this expression is used in the Bible. In the Messianic Scriptures Yahshua is referred to by demoniacs as “Son of HaElyon” in Mk. 5:7; Luke 8:28; Acts 16:17; Hebrews 7:1). Traditional Judaism believes Malchizedek as the most honored of Noah’s children “Shem” (Babylonian Talmud, N’darim 32b). The Sages say he was called Malchizedek because he was the king of the future site of the Temple of G-d in Jerusalem, and as the most honored of Noah’s children he was made the Priest in Jerusalem.
Traditional Judaism explains that by Abraham paying tithes to Malchizedek it indicates that Malchizedek is greater than Abraham and greater than the Levitical Priesthood because the Levites were still in the lions of Abraham and therefore they too paid tithes to Malchizedek. Also that Malchizedek blessed Abraham shows he was greater than Abraham was. All this indicates Malchizedek occupied a superior priesthood over the Levitical system.
Yahshua is compared with Malki-Tzedek (Malchizedek) in Psalms 110:4 which is quoted in Hebrews 5:6, 10; 6:20; 7:11, 17. He is King of Shalem and the author of Hebrews give a drash on how great he was (v.4) in a step to showing how great Yahshua is.
Shalem is akin to Shalom means no only “peace” but health, integrity, and wholeness. In Isaiah 9:5-6(6-7) we see one of the most important Tanakh (OT) prophecies of the Messiah. He is called “Prince of Peace” (sar-shalom).
Malchizedek had no recorded antecedents, father, mother, ancestry, birth or death. This enables the author of Hebrews to develop a Midrash that Malki-Tzedek continues as a Cohen (Priest) for all time, Like the Son of G-d. Yahshua had no human father (Matthew 1:18-25) and who existed in the Word before His birth.
Malchizedek was both King and Priest. Traditional Judaism separates the offices. One mans a king another a High Priest. Malchizedek held both offices as Yahshua holds both offices. Therefore he is a Priest after the Order of Malchizedek which is priesthood greater than the Levitical Priesthood. In the Book of Revelation Levites are now listed as a tribe whereas they were not earlier because Yahshua occupies the Kingship and office of Cohen Gadol (High Priest) as did Malchizedek and the Levitical system has been superceded by a better priesthood.
I could go on and on with much detailed information but I think this is sufficient to illustrate Melchizedek’s place in the biblical and extra Jewish writings.
As to mission he was to establish a Priest/King dynasty so that legally Yahshua could hold the offices of King/Priest jointly over Israel in order to legitimize His reign.