Person

Melchizedek

A mysterious priest-king who appears in Genesis 14 as "king of Salem" and "priest of God Most High." He blesses Abram and receives a tithe from him. He surfaces twice more in the canon. Psalm 110:4 names the Messiah a "priest forever according to the order of Melchizedek." Hebrews 5-7 develops the typology at length. It treats Melchizedek as a figure whose priesthood is greater than the later Levitical / Aaronic priesthood and whose office foreshadows Christ's eternal high-priestly ministry.

Biblical appearances

Genesis 14:18-20, Melchizedek meets Abram as he returns from defeating the kings. He brings out bread and wine, blesses Abram as "priest of God Most High," and Abram gives him a tenth of all.
Psalm 110:4, a Davidic / Messianic psalm: "You are a priest forever according to the order of Melchizedek." This is cited more often in the New Testament than any other Old Testament verse.
Hebrews 5:6, 5:10, 6:20, 7:1-17, the extended typological argument. Melchizedek's priesthood is not by ancestral lineage. He has no recorded beginning or end of days. He is therefore a fitting type of Christ's eternal priesthood. The Levites (descendants of Abraham) tithed through Abraham to Melchizedek, which shows Melchizedek's superiority.

Theological significance

Christological type. Hebrews reads Melchizedek as a deliberate prefigurement of Christ's high-priestly office: eternal, royal, non-Levitical, and mediating a better covenant.
Argument from priesthood-change. A change of priesthood requires a change of law (Heb 7:11-12). Because Christ is enthroned as priest "according to the order of Melchizedek," the Levitical priesthood, and the legal system bound to it, is superseded. This is the argumentative spine of Are Christians Still Under The Law (ris3n).
Royal-priestly union. Melchizedek combines kingship and priesthood in one office. This prefigures Christ as both King and Priest, something the Levitical line (held strictly separate from the Davidic kingly line) could not.
Independence from Sinai. Melchizedek's priesthood predates the Mosaic Law by centuries. That shows priestly mediation between God and humanity is not rooted in or limited to the Sinaitic covenant.

Interpretive options

Typological figure (mainstream Protestant, Catholic, and patristic): a real historical priest-king whose office and silence of genealogy make him an apt type of Christ.
Christophany / pre-incarnate appearance of the Son: a minority view (some patristics, some modern interpreters) that Melchizedek is the pre-incarnate Christ. Held in tension with Heb 7:3 ("made like the Son of God"), which seems to distinguish them.
Angelic / supernatural figure: extracanonical Second Temple traditions (for example, the 11Q13 Melchizedek scroll at Qumran) develop Melchizedek as a heavenly redeemer figure. Canonical Hebrews does not adopt this, but it is informative for backdrop.