Aaron was to offer several specific sacrifices and anoint the altar, the tent, and the mercy seat within the Holy Place with the blood of these sacrifices to make atonement for all the people.
Part of this ceremony involved identifying two goats, one to be sacrificed and the other to have the sins of the people poured out over it and then to be released into the wilderness. Like the birds in Chapter 14, the goat being sacrificed represented Christ making the ultimate atonement for our sin, while the scapegoat, the one released in the wilderness, represented His resurrection.
Like many of the Old Testament sacrifices and rituals, the day of atonement drives home the truth that all have sinned and that sin must be atoned for with a sacrifice. As believers in Jesus Christ, we recognize that Christ fulfilled, once and forever, the need for atonement for sin. His perfect sacrifice, as the only One who never sinned, on behalf of all of us who have, forever ended our need to make atonement for ourselves through rituals or good works.
Instead, now, we rejoice that our sins have been forever covered by the blood of Jesus, and we demonstrate the change He has made in our lives by reflecting the love He gave us to others.