Verses 1-10
7:1-10:18 CHRIST'S PRIESTHOOD AND SACRIFICE
The priesthood of Melchizedek (7:1-10)
Jesus Christ's high priesthood is far superior to Aaron's. Christ belongs to the priestly order of Melchizedek, a priesthood that existed before, and is far higher than, that of Aaron. (For the background concerning Melchizedek see Genesis 14:17-24 and Psa_110:4.) Melchizedek was both a priest and a king, a combination not allowed in the Aaronic priesthood. In the Levitical order, people kept strict records of ancestry, birth and death, to confirm a person's right to be a priest (cf. Ezra 2:62-63; Nehemiah 7:63-65), but no such records exist for Melchizedek. They are not necessary, because his priesthood is not limited by time or Levitical laws. This is clearly seen in Abraham's acknowledgment of Melchizedek as the representative of the Most High God long before the Levitical law was given. In all these things the priesthood of Melchizedek foreshadowed that of Christ (7:1-3).
Abraham was a great man, being the father of all Israel, but Melchizedek was greater, for he blessed Abraham. The one who blesses must be greater than the one blessed. Abraham acknowledged Melchizedek's superiority by giving him a tithe (one tenth) of his goods. Under the Levitical law ordinary Israelites paid tithes to the Levites, their religious representatives. But the Levites, being in Abraham (so to speak), paid tithes to Melchizedek. In this they acknowledged the superiority of his priesthood to theirs (4-10).
Verses 11-28
Christ, a priest like Melchizedek (7:11-28)
The necessity for a new priesthood under Christ shows that the Levitical priesthood (and with it the law of Moses) failed to bring perfection. Therefore, the new priest belongs not to Aaron's order but to Melchizedek's (11-12). Christ could not be a priest in the Levitical order, because he was not from the tribe of Levi. He was from Judah, a tribe that had no part in priestly affairs (13-14).
Laws concerning physical birth and age determined who could be Levitical priests and how long they could serve. The priesthood of Christ does not depend on human ancestry, nor, because of his indestructible life, can it be brought to an end (15-17). Christ has done what the Levitical system could not do. He has brought perfection and given people access to God's presence (18-19).
The Levitical priesthood lacked permanence and certainty, but not so Christ's priesthood. It is guaranteed by the oath of God (20-22). Christ is not like the Levitical priests, who needed others to take their place when they died. He lives on as a priest for ever, bringing people to God and giving them God's saving help (23-25). Because of the purity of his character, life and work, Christ is worthy of the place of highest honour. Levitical priests could not, with all the sacrifices they offered, make others perfect, because they themselves were sinners. Christ, God's sinless Son and great high priest, makes people perfect for ever by one sacrifice, the sacrifice of himself (26-28).