Verse 7 says that the priest offered (or brought) blood for himself and for the people's sins, and verse 23 underscores that the part of the ceremony involving bringing blood into the Most Holy Place was for purification or cleansing of the objects. This idea is also found in verse 22, which says that according to the law almost all things are purified with blood.
The Levitical priest used animal blood, but our High Priest entered the Holy of Holies in heaven with His own blood. His blood provides an entrance into the presence of the Supreme God. I don't know if you've ever thought about it, but verse 23 says the heavenly things had to be purified. It's as though simply being in the same universe as humanity meant they had to be cleansed. But Christ's blood provides a cleansing so complete that we now can come boldly to the throne of grace, that we may obtain mercy and find grace to help in time of need. His blood appeases the Father, so we can draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience.
Please begin turning to Hebrews 9. The book of Hebrews has been described as the Leviticus of the New Testament. A main purpose of Hebrews was to help the church - particularly those of a Jewish background - to understand the Scriptures through the lens of Christ's life, death, and High Priesthood. Chapter 9 contains the New Testament explanation of the Day of Atonement. If there were a confirmation that sins will be laid on the head of either the Devil or one of his minions, and that he will bear them, there could hardly be a more fitting place to make note of it than Hebrews 9.
However, the author does not even hint at Satan's involvement with atonement in any way. Instead, the flow of the chapter reinforces Christ's fulfillment of the Day of Atonement at every point. Hebrews 9:22-25 describes the purifying of the holy place, which is what the first goat accomplished. No sins were confessed on it, so its blood allowed entrance into the Holy of Holies, even as Jesus entered the heavenly Holy of Holies with His own pure blood.
