The annual day of atoning was necessary because of two things: the holiness of God and the sinfulness of men. Both of those realities were seen clearly in the divine execution of Nadab and Abihu (Leviticus 10:1-2 and 16:1). Even "well meaning" religious activities are rejected by God when those activities are self-righteous efforts rather than simple faith-filled responses to His will. So, while many sacrifices were offered daily throughout the whole year, there was one day that was set aside for a general sacrifice for all sins of all people for the whole year. On the 10th day of the month, the high priest was to go into the Holy of Holies to atone for his own sins and then for the sins of the people. This ritual was highly typical. There were many activities during the Day of Atonement that pointed to the day when the Great High Priest, the Lord Jesus Christ, would offer Himself for the sins of all men for all time.
Each year as Aaron stood behind the Ark of the Covenant and sprinkled the blood upon the lid, the presence of God was manifested there in a cloud. Now, unlike the Messiah, Aaron had to offer the blood of a young bull to atone for his own sin prior to offering the blood of the sacrificial goat for the all of the sins of the people (Leviticus 16:16, 30 and 34). Of course, Jesus had no sin of His own, so He simply "became sin" on the cross and offered Himself for us.
The most outstanding part of the day's ritual was the handling of the two goats. By chance (Ruth 2:3 and Ecclesiastes 9:11) one goat was selected to be killed as a sin offering and the other was left to be set free in the wilderness. Both goats represented the ugliness that made the day necessary in the first place.
The dead goat represented the sinner and the scapegoat represented the sin. The punishment that God owed to the people was laid on the sacrificial goat... thereby rolling God's wrath against them back for another year as they waited for the sufficient sacrifice that had been promised (Genesis 3:15, 22:8 and 49:10). Their sins were metaphorically placed on the scapegoat and were thereby taken away. The destination of the scapegoat represented the sea of God's forgetfulness (Micah 7:19). Yom Kippur... the Day of Atonement; without atonement there could be no peace with God - then, or now.