What is the Day of Atonement then?
“The Lord spoke to Moses after the death of two of Aaron’s sons when they approached the presence of the Lord and died. The Lord said to Moses, “Tell your brother Aaron that he may not come whenever he wants into the holy place behind the curtain in front of the mercy seat on the ark or else he will die, because I appear in the cloud above the mercy seat. “Aaron is to enter the most holy place in this way: with a young bull for a sin offering and a ram for a burnt offering. He is to wear a holy linen tunic, and linen undergarments are to be on his body. He is to tie a linen sash around him and wrap his head with a linen turban. These are holy garments; he must bathe his body with water before he wears them. He is to take from the Israelite community two male goats for a sin offering and one ram for a burnt offering. “Aaron will present the bull for his sin offering and make atonement for himself and his household. Next he will take the two goats and place them before the Lord at the entrance to the tent of meeting. After Aaron casts lots for the two goats, one lot for the Lord and the other for an uninhabitable place, he is to present the goat chosen by lot for the Lord and sacrifice it as a sin offering. But the goat chosen by lot for an uninhabitable place is to be presented alive before the Lord to make atonement with it by sending it into the wilderness for an uninhabitable place. “When Aaron presents the bull for his sin offering and makes atonement for himself and his household, he will slaughter the bull for his sin offering. Then he is to take a firepan full of blazing coals from the altar before the Lord and two handfuls of finely ground fragrant incense, and bring them inside the curtain. He is to put the incense on the fire before the Lord, so that the cloud of incense covers the mercy seat that is over the testimony, or else he will die. He is to take some of the bull’s blood and sprinkle it with his finger against the east side of the mercy seat; then he will sprinkle some of the blood with his finger before the mercy seat seven times. “When he slaughters the male goat for the people’s sin offering and brings its blood inside the curtain, he will do the same with its blood as he did with the bull’s blood: He is to sprinkle it against the mercy seat and in front of it. He will make atonement for the most holy place in this way for all their sins because of the Israelites’ impurities and rebellious acts. He will do the same for the tent of meeting that remains among them, because it is surrounded by their impurities. No one may be in the tent of meeting from the time he enters to make atonement in the most holy place until he leaves after he has made atonement for himself, his household, and the whole assembly of Israel. Then he will go out to the altar that is before the Lord and make atonement for it. He is to take some of the bull’s blood and some of the goat’s blood and put it on the horns on all sides of the altar. He is to sprinkle some of the blood on it with his finger seven times to cleanse and set it apart from the Israelites’ impurities. “When he has finished making atonement for the most holy place, the tent of meeting, and the altar, he is to present the live male goat. Aaron will lay both his hands on the head of the live goat and confess over it all the Israelites’ iniquities and rebellious acts — all their sins. He is to put them on the goat’s head and send it away into the wilderness by the man appointed for the task. The goat will carry all their iniquities into a desolate land, and the man will release it there. “Then Aaron is to enter the tent of meeting, take off the linen garments he wore when he entered the most holy place, and leave them there. He will bathe his body with water in a holy place and put on his clothes. Then he must go out and sacrifice his burnt offering and the people’s burnt offering; he will make atonement for himself and for the people. He is to burn the fat of the sin offering on the altar. The man who released the goat for an uninhabitable place is to wash his clothes and bathe his body with water; afterward he may reenter the camp. The bull for the sin offering and the goat for the sin offering, whose blood was brought into the most holy place to make atonement, must be brought outside the camp and their hide, flesh, and waste burned. The one who burns them is to wash his clothes and bathe himself with water; afterward he may reenter the camp. “This is to be a permanent statute for you: In the seventh month, on the tenth day of the month you are to practice self-denial and do no work, both the native and the alien who resides among you. Atonement will be made for you on this day to cleanse you, and you will be clean from all your sins before the Lord. It is a Sabbath of complete rest for you, and you must practice self-denial; it is a permanent statute. The priest who is anointed and ordained to serve as high priest in place of his father will make atonement. He will put on the linen garments, the holy garments, and make atonement for the most holy place. He will make atonement for the tent of meeting and the altar and will make atonement for the priests and all the people of the assembly. This is to be a permanent statute for you, to make atonement for the Israelites once a year because of all their sins.” And all this was done as the Lord commanded Moses.”
Leviticus 16:1-34 CSB
Then if you read Hebrews this is explained how Jesus Christ fulfilled this Feast and is the once and for all sacrifice for sin and the High Priest that entered the Most Holy Place in Heaven and presented His own blood at the Heavenly altar for us once and for all.
“Since the law has only a shadow of the good things to come, and not the reality itself of those things, it can never perfect the worshipers by the same sacrifices they continually offer year after year. Otherwise, wouldn’t they have stopped being offered, since the worshipers, purified once and for all, would no longer have any consciousness of sins? But in the sacrifices there is a reminder of sins year after year. For it is impossible for the blood of bulls and goats to take away sins. Therefore, as he was coming into the world, he said: You did not desire sacrifice and offering, but you prepared a body for me. You did not delight in whole burnt offerings and sin offerings. Then I said, “See — it is written about me in the scroll — I have come to do your will, God.” After he says above, You did not desire or delight in sacrifices and offerings, whole burnt offerings and sin offerings (which are offered according to the law), he then says, See, I have come to do your will. He takes away the first to establish the second. By this will, we have been sanctified through the offering of the body of Jesus Christ once for all time. Every priest stands day after day ministering and offering the same sacrifices time after time, which can never take away sins. But this man, after offering one sacrifice for sins forever, sat down at the right hand of God. He is now waiting until his enemies are made his footstool. For by one offering he has perfected forever those who are sanctified. The Holy Spirit also testifies to us about this. For after he says: This is the covenant I will make with them after those days, the Lord says, I will put my laws on their hearts and write them on their minds, and I will never again remember their sins and their lawless acts. Now where there is forgiveness of these, there is no longer an offering for sin. Therefore, brothers and sisters, since we have boldness to enter the sanctuary through the blood of Jesus — he has inaugurated for us a new and living way through the curtain (that is, through his flesh) — and since we have a great high priest over the house of God, let us draw near with a true heart in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodies washed in pure water. Let us hold on to the confession of our hope without wavering, since he who promised is faithful. And let us consider one another in order to provoke love and good works, not neglecting to gather together, as some are in the habit of doing, but encouraging each other, and all the more as you see the day approaching. For if we deliberately go on sinning after receiving the knowledge of the truth, there no longer remains a sacrifice for sins, but a terrifying expectation of judgment and the fury of a fire about to consume the adversaries. Anyone who disregarded the law of Moses died without mercy, based on the testimony of two or three witnesses. How much worse punishment do you think one will deserve who has trampled on the Son of God, who has regarded as profane the blood of the covenant by which he was sanctified, and who has insulted the Spirit of grace? For we know the one who has said, Vengeance belongs to me; I will repay, and again, The Lord will judge his people. It is a terrifying thing to fall into the hands of the living God. Remember the earlier days when, after you had been enlightened, you endured a hard struggle with sufferings. Sometimes you were publicly exposed to taunts and afflictions, and at other times you were companions of those who were treated that way. For you sympathized with the prisoners and accepted with joy the confiscation of your possessions, because you know that you yourselves have a better and enduring possession. So don’t throw away your confidence, which has a great reward. For you need endurance, so that after you have done God’s will, you may receive what was promised. For yet in a very little while, the Coming One will come and not delay. But my righteous one will live by faith; and if he draws back, I have no pleasure in him. But we are not those who draw back and are destroyed, but those who have faith and are saved.”
Hebrews 10:1-39 CSB