The Day of Atonement in Leviticus chapter 16 involves a blood sacrifice to purify the high priest, the tabernacle, and the people of Israel from their sins. The scapegoat represents the removal of sin, while the blood of the bull and goat symbolize the substitutionary atonement of Christ. The high priest must be purified before entering the holy place, and the tabernacle requires purification due to the uncleanness of the people.