Melchizedek appears only once in the Bible, briefly in Genesis 14. He was a local king-priest who came to bless and congratulate Abraham after his defeat of Chedorlaomer who had taken Lot hostage. Like Abraham himself Melchisedek appears to have taken no part in the original fight between Chedorlaomer and the King of Sodom which had led to Lot – resident in Sodom – being captured.
17 After his return from the defeat of Chedorlaomer and the kings who were with him, the king of Sodom went out to meet him at the Valley of Shaveh (that is, the King’s Valley). 18 And Melchizedek 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, Possessor of heaven and earth; 20 and blessed be God Most High, who has delivered your enemies into your hand!” And Abram gave him a tenth of everything. 21 And the king of Sodom said to Abram, “Give me the persons, but take the goods for yourself.” 22 But Abram said to the king of Sodom, “I have lifted my hand to the Lord, God Most High, Possessor of heaven and earth, 23 that I would not take a thread or a sandal strap or anything that is yours, lest you should say, ‘I have made Abram rich.’ 24 I will take nothing but what the young men have eaten, and the share of the men who went with me. Let Aner, Eshcol, and Mamre take their share.” (Genesis 14:17-24 ESV)
And that is it. We know nothing further than what is in the passage, other than the name Melchisedek means “king of righteousness”.
Melchizedek in Psalm 110
The only other mention of Melchizedek is in Psalm 110
The Lord has sworn and will not change his mind, “You are a priest forever after the order of Melchizedek.” (Psalm 110:4)
Psalm 110, which begins “The LORD said to my Lord” is the most frequently referenced psalm in the New Testament. It is taken as a Messianic psalm and prophecy of an anointed king-priest in those references. This interpretation is common also in Jewish commentary.
Melchizedek in Hebrews
In Hebrews the author develops from the example of Melchizedek an argument for the primacy of Christ as king-priest over the Aaronic priests:
5:6 as he says also in another place, “You are a priest forever, after the order of Melchizedek.”
5;10 being designated by God a high priest after the order of Melchizedek.
6:20 where Jesus has gone as a forerunner on our behalf, having become a high priest forever after the order of Melchizedek.
7:1 For this Melchizedek, king of Salem, priest of the Most High God, met Abraham returning from the slaughter of the kings and blessed him,
7:10 for he was still in the loins of his ancestor when Melchizedek met him.
7:11 Now if perfection had been attainable through the Levitical 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 Melchizedek, rather than one named after the order of Aaron?
7:15 This becomes even more evident when another priest arises in the likeness of Melchizedek,
7:17 For it is witnessed of him, “You are a priest forever, after the order of Melchizedek.”