Hebrews 7-10: A Better Priest

In these chapters, the writer of Hebrews introduces Melchizedek.  Melchizedek was described as priest of the God most High.

   After Abram returned from defeating Kedorlaomer and the kings allied with him, the king of Sodom came out to meet him in the Valley of Shaveh (that is, the King’s Valley).
   Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High, and he blessed Abram, saying,
   “Blessed be Abram by God Most High,
   Creator of heaven and earth.
   And blessed be God Most High,
   who delivered your enemies into your hand.”
   Then Abram gave him a tenth of everything. - Gen. 14:17-20 NIV

Melchizedek preceded the Aaronic priesthood.  He was a priest of God.  There have been many priests descended from Abraham, but their representation before God was temporary,  since death prevented them from continuing in office; but because Jesus lives forever, he has a permanent priesthood. Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them. (Heb. 7:23-25 NIV)  This priest, Jesus, represents the new covenant that God made with his people.  
This is the covenant I will make with the house of Israel
   after that time, declares the Lord.
I will put my laws in their minds
   and write them on their hearts.
I will be their God,
   and they will be my people. - Heb. 8:10 NIV

Instead of an animal sacrifice, Christ became a living sacrifice.  Unlike the ritual sacrifices made by the priests, Christ made an eternal sacrifice.  Just as man is destined to die once, and after that to face judgment, so Christ was sacrificed once to take away the sins of many people; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him.(Heb. 9:27-28 NIV)  Christ's one time sacrifice covered sins, and now, all who believe, can enter the Most Holy Place by the blood of Jesus, with hearts that have been cleansed by his blood.