In the OT, a man would bring a sin offering to the priest, he would place his hand on the head of the animal, confess his sin before the priest, and the priest would sacrifice the offering. It was as if the sin was transferred to the animal, who received death, the consequence of sin in the place of the person.
At the Great Day of Atonement, the High Priest would sacrifice a Ram as himself, a goat for the people, and drive the scapegoat into the wilderness. The red ribbon on the scapegoat would turn white when the atonement was complete. The priest would take the blood of the sacrifice into the Holy of Holies, before the Mercy Seat, where it would become holy, and a source of life. The High Priest would then take it back out, and sprinkle it on the parts of the Temple, which represented the parts of creation, thus restoring the bonds of creation and pushing back the decay and death that came with the people's sins.
Christ is the true High Priest. He sacrificed Himself, ascended into the Holy of Holies, and is coming again to recreate the world.
When we confess our sins before the priest, it is as if the priest bears them. Then, in the Offertory, the priest rubs his hand of the Lamb, it is as if he is placing our sins that he has taken in confession upon the Lamb, upon Christ. The Liturgy is a making present of Calvary, and so our sins are placed upon Christ, who took upon Himself the sins of the world, and defeated sin and death upon the Cross, and rose in life. Our offering to God of bread and wine is returned to us as the Body and Blood of Christ, who ascended into Heaven, into the Holy of Holies, that comes to us out of the Sanctuary, out of the Holy of Holies to give us life.
The whole Liturgy is a participation the true Day of Atonement, but, in the Coptic rite at least, the absolution also takes the form of the Day of Atonement to show us clearly and concisely what we are participating in. The priest ascends to the Sanctuary while the chanters chant a wordless hymn, just as the chanters of the old testament did when the High Priest ascended to the Sanctuary, and then the priest comes out to give the absolution.