Albert Barnes Commentary Leviticus 16:33-34

"and he shall make atonement for the holy sanctuary; and he shall make atonement for the tent of meeting and for the altar; and he shall make atonement for the priests and for all the people of the assembly. And this shall be an everlasting statute unto you, to make atonement for the children of Israel because of all their sins once in the year. And he did as Jehovah commanded Moses." — Leviticus 16:33-34 (ASV)

A summary of what was done on the Day of Atonement.

The Day was intended as an occasion for expressing more completely than could be done in the ordinary sacrifices the spiritual truth of atonement, with a fuller acknowledgment of the sinfulness and weakness of man and of the corruptible nature of all earthly things, even of those most solemnly consecrated and devoted to the service of God.

Its observances especially set forth, through the high priest’s entrance into the Holy of Holies, that atonement could only be effected before the throne of Yahweh Himself (Mark 2:7–10; Hebrews 4:16, and others). Furthermore, the goat sent into the wilderness signified that the sins atoned for were not only forgiven but carried wholly away (see the note on Leviticus 16:22).

The rites were a solemn gathering up of all other rites of atonement, making them point more expressively to the coming revelation of God’s gracious purpose to man: sending His Son to be delivered for our offences, and to rise again for our justification; to be our great high priest forever after the order of Melchisedec; and to enter for us within the veil (Romans 4:25; Hebrews 6:20).

The Day of Atonement expanded the meaning of every sin offering, just as the services for Good Friday and Ash Wednesday expand the meaning of our litany days throughout the year, and Easter Day expands the meaning of our Sundays.