1 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. 5 And those descendants of Levi who receive the priestly office have a commandment in the law to take tithes from the people, that is, from their brethren, though these also are descended from Abraham. 6 But this man who has not their genealogy received tithes from Abraham and blessed him who had the promises. 7 It is beyond dispute that the inferior is blessed by the superior. 8 Here tithes are received by mortal men; there, by one of whom it is testified that he lives. 9 One might even say that Levi himself, who receives tithes, paid tithes through Abraham, 10 for he was still in the loins of his ancestor when Melchiz'edek met him.
The story of Melchizedek's priesthood is mentioned in Genesis 14:17-20. His priesthood differed from the Aaronic priesthood in a number of ways. First Melchizedek had no genealogy and thus his priesthood was understood to be eternal. In chapter seven of Hebrews we see five qualities of Melchizedek's priesthood: It is a priesthood of righteousness, peace, a royal priesthood (Melchizedek was a king), a personal priesthood rather than an inherited priesthood, and it is eternal, since it has no genealogy, beginning or end
The order of Melchizedek indicates that Christ was not appointed to the Aaronic priesthood of the old covenant but to a priesthood that would replace it and would be greater, just as Melchizedek himself was greater than Aaron and even Abraham himself.
The priest was the only one who could present a gift to God (cf. Hebrews 5:1). He could do so, because he had to be chosen to be God's servant. As the minister of God, the priest had special access to God's presence and could approach more closely than ordinary worshipers. He was the intermediary between God and the people. He represented the people to God and God to the people.
Christ's position as the great high priest enabled him to play a special role in our redemption. Because he was appointed priest, Christ was able to offer his death as a sacrifice for others. His actions counted for others because a high priest is able to offer atoning sacrifices for sin to God on behalf of those he represents.
Jesus is our great and eternal High Priest who lives forever. He is the high priest who is himself sinless and never needs to offer any sacrifice for his own sin. In the offering of himself he made the perfect sacrifice which once and for all opened the way to God. No other sacrifice need be made.
"Lord Jesus Christ, you are our eternal high priest and intercessor. Your blood cleanses us from all stain of sin and guilt. Purify my heart and cleanse my mind that I my thoughts and actions may be pleasing to you and my prayer be acceptable as a sacrifice of praise and worship."