How is Christ our Priest?

Sam Waldron explains in this video that the preeminent function of a priest was to offer sacrifice. This sacrifice was made to satisfy our sin and its guilt. This is the language of Hebrews 5. The great function of Christ as a Priest was to offer a sacrifice and by that sacrifice, to expiate the sins of His people. 

The work of a Priest has two aspects: first, the aspect of the offering of the sacrifice. Then, there is the blood offering to God to satisfy sins for those the priest represents. Christ offers Himself to God. He makes a way for His people to be reconciled. 

Hebrews 7:26-27 (NKJV) - "For such a High Priest was fitting for us, who is holy, harmless, undefiled, separate from sinners, and has become higher than the heavens; who does not need daily, as those high priests, to offer up sacrifices, first for His own sins and then for the people’s, for this He did once for all when He offered up Himself."

The preeminent function of a priest was offering sacrifice. And the preeminent sacrifice was sacrifice to expiate or satisfy for sin and its guilt. And this is certainly the language of Hebrews 5, which says what priest is there that doesn't offer some sacrifice? And so the great function of Christ as a priest is to offer a sacrifice and on the basis of that sacrifice to propitiate or expiate the sins, the guilt of the sins of his people. Now that work of a priest has two functions or two aspects or two phases I guess you might say.

There is the phase of the actual offering of the sacrifice, the slaughtering of the sacrifice, and then there is the phase in which the blood of that sacrifice is presented to God formally as a means of satisfying for the sins of those whom the priest has represented. Now Christ, of course, is both victim and priest. He offers himself to God, is the pregnant language of scripture. He offers himself to God, and then in returning to heaven, He offers Himself in heaven, He offers the fruits of that sacrifice, His blood, His shed blood to God in order to make a way for His people to come into the holiest of all. The wonderful imagery, the grand imagery of the Old Testament is important here.

The priest offers the sacrifice and then comes with blood once a year to the holiest of all, the Holy of Holies, and there He sprinkles that blood on the mercy seat. The book of Hebrews teaches that it's through that that we are made objectively and perfectly holy by Christ so that we may also enter that place into which nothing unclean may come. So we have an objective perfect holiness or righteousness in Christ which enables us to come into the holiest of all and not be unfit for the thrice holy presence of God.