A Facebook friend asked me about this mysterious figure:

I'm curious: why did this man who is mentioned in two verses in Genesis and one in Psalms (which is then quoted in Hebrews) became such a big deal? How did he get to his prominent position as having an everlasting priesthood? How do we know he was a priest of the same God we worship?

How did the Jews come to identify him as “a priest forever, in the line of Melchizedek” that we see in Psalms? How did it come about that he was included in the canon of the Mass? We don't mention any of the other priests, like Aaron.

These are good and fascinating questions. Here are the relevant scriptural passages:

Genesis 14:18-19 (RSV) And Mel-chiz'edek king of Salem brought out bread and wine; he was priest of God Most High. [19] And he blessed him and said, “Blessed be Abram by God Most High, maker of heaven and earth;

Psalm 110:4 The LORD has sworn and will not change his mind, “You are a priest for ever after the order of Melchiz'edek.”

Hebrews 7:1-4 For this Melchiz'edek, king of Salem, priest of the Most High God, met Abraham returning from the slaughter of the kings and blessed him; [2] and to him Abraham apportioned a tenth part of everything. He is first, by translation of his name, king of righteousness, and then he is also king of Salem, that is, king of peace. [3] He is without father or mother or genealogy, and has neither beginning of days nor end of life, but resembling the Son of God he continues a priest for ever. [4] See how great he is! Abraham the patriarch gave him a tithe of the spoils. (cf. Heb 5:6, 10; 6:20; 7:5-10, 12-17)

Hebrews 7:11 Now if perfection had been attainable through the Levit'ical priesthood (for under it the people received the law), what further need would there have been for another priest to arise after the order of Melchiz'edek, rather than one named after the order of Aaron?

The 1911 Catholic Encyclopedia article (citing Hebrews 7:3) notes that he was a prototype of our Lord Jesus. It adds:

The silence of Scripture about the facts of Melchisedech's birth and death was part of the divine plan to make him prefigure more strikingly the mysteries of Christ's generation, the eternity of His priesthood.

But why did the ancient Jews (who would, of course, reject the Christian messianic interpretation) give him such prominence in the first place? The 1906 Jewish Encyclopedia gives us a good idea:

To the Jewish propagandists of Alexandria, who were eager to win proselytes for Judaism without submitting them to the rite of circumcision, Melchizedek appealed with especial force as a type of the monotheist of the pre-Abrahamic time or of non-Jewish race, like Enoch. Like Enoch, too, he was apotheosized. He was placed in the same category with Elijah, the Messiah ben Joseph, and the Messiah ben David . . . The singular feature of supernatural origin is ascribed to all four, . . .

The same source, under the entry for “Shem” (Noah’s oldest son), provides what was the traditional rabbinic explanation:

The Rabbis identify Shem with Melchizedek, King of Salem, . . . who came to meet Abraham after the latter had defeated the four kings led by Chedorlaomer (Gen. xiv. 18-20). According to this account, Shem, as a priest, came to Jerusalem (with which Salem is identified by the Rabbis), of which city he became king, it being the proper place for the establishment of the cult of Yhwh. He went to meet Abraham to show him that he was not angry with him for having killed the Elamites, his descendants (Midr. Agadah on Gen. l.c.). . . .

Dr. Rabbi Joshua Garroway, in his article, “Who Assumed Melchizedek’s Priesthood?” at Torah.com, elaborates, as to the rabbinic interpretation of Psalm 110:

In other words, “You, Abraham, have become a priest because of what Melchizedek mistakenly said.” The coup de grace in this reinterpretation comes when Rabbi Ishmael notes that Gen. 14:18 can be read in a limited sense: yes, Melchizedek was a priest, but it does not say that his descendants would also be priests.

Thus, the Talmud is able to have its cake and eat it too. Melchizedek can be a priest, even the first priest, just as the Torah says, but the right to the priesthood thereafter is limited to the descendants of Abraham through Levi and Aaron.

Dr. Garroway further comments:

The rabbis, . . . simply could not countenance the idea that this non-Levite is called a priest of God the Most High—and in Jerusalem, no less! The Torah later insists that God’s priesthood belongs perpetually to the descendants of Levi through Aaron, so how can there be an eternal priestly order through Melchizedek?

The prominence assigned to this seemingly shadowy figure by the Jews is perhaps summed up in the entry from The Universal Jewish Encyclopedia (edited by Isaac Landman, New York: 1942):

Because Melchizedek united the royalty with the priesthood, like the kings of the ancient Near East, he became the prototype for the priestly rulers of the Hasmonean dynasty (cf. Ps. 110:4). . . . Abraham is alleged to have learned the practise of charity from Melchizedek (Midrash Ps. 37). Philo regards Melchizedek  as “the logos, the priest whose inheritance is the true God.” Melchizedek assisted David in writing the Psalms (Ps. no; cf. B.B. 14b et seq.).

Lastly, why is Melchizedek mentioned in the Catholic Mass? Shawn R. Tribe, in an article on “Saints of the Roman Canon” provides a plausible reason:

Here we see three figures of the Old Testament mentioned: Abel, Abraham and Melchizedek. Each of these offered to God sacrifices which were pleasing to Him (Abel: Genesis 4:4, Melchizedek, Genesis 14:18-20, Abraham: Genesis 22), and the same is asked of the sacrifice made present within the Mass.