In Judaism, the priesthood of Melchizedek is a symbolic line combining royal and religious authority: kings who act as mediators between God and their people. In Abraham's time, Melchizedek was both king of Salem and priest of the Most High. His symbolic descendants included both David and the expected Messiah.
Unlike the Levitical priesthood, whose members were all required by Mosaic law to be descendants of Aaron, the priesthood of Melchizedek is nonhereditary. Melchizedek, the first identified priest in the Pentateuch, long predates Aaron: he came out to meet Abraham as he returned from battle, blessed him with bread and wine and received tithes from him, as reported in Genesis 14. In some interpretations, this act represents the conferral of the priesthood upon the line of Abraham, possibly because Abraham chose to be sustained by Melchizedek's holy offering rather than the material spoils of his victory offered by his other royal allies. Melchizedek's name translates as "King of Righteousness" or "King of Peace," epithets echoed in the names the prophecies of Isaiah use for the awaited Messiah.
In Christianity, Melchizedek is considered a symbolic precursor to Christ. In the New Testament, Hebrews 7 argues for Christ as the inheritor of the "order of Melchizedek," providing a rationale for Jewish Christians in Jerusalem to accept Christ as eternal High Priest despite his not having been a Levite. As Melchizedek offered bread and wine to Abraham, so Christ offered bread and wine to his disciples at the Last Supper. Therefore, all Roman Catholic priests are considered part of the order of Melchizedek, which is also the "priesthood of Christ."
In Mormonism, the Melchizedek priesthood refers to the priesthood held by every adult male member of the Church of Latter-Day Saints. The responsibilities of this priesthood include presiding over the family unit and giving blessings, guidance and comfort to one's wife and children, as well as conferring blessings on other Mormons.