Here is the most important thing about Yom Kippur:
We do not assist in our atonement.
If you read Leviticus 16, it lists many rituals and sacrifices which must be performed on this most holy day, all of which are to atone for and cleanse the people of Israel from their sins. And without exception, every cleansing ritual is performed by the Kohen HaGadol (the High Priest) ALONE. No one else is even allowed to be in the Mish’kan (Tabernacle) during the event, and the only role that other people have is to lead the live goat to the wilderness, and to burn the leftover pieces of the sacrifices outside the camp. But the actual sacrificing of the animals, the sprinkling of their blood, the offering of their fat and organs to God, the transferring of sins and iniquity onto the head of the live goat—everything that actually makes atonement and cleansing of sins is performed by the Kohen HaGadol without assistance from the people for whom he makes atonement.
This is made most clear at the end of the chapter, when God finally turns to His expectations of the general population of Israel. God’s instructions are that the people must rest from work and treat Yom Kippur as a full-on Shabbat (stopping from activities), and He tells them to “afflict your souls” (or “humble your souls” or “deny yourselves”—a concept biblically linked with fasting, cf. Isa. 58:5 & Psa. 35:13). And then God says that the reason for this is:
Leviticus 16:30 (JPS 1917)
For on this day shall atonement be made for you, to cleanse you; from all your sins shall ye be clean before the LORD.
Note the wording here. God does not say that the people must afflict themselves to get atoned for. Rather, He says that atonement is made for them on this day, so they need to afflict themselves. Atonement is made FOR YOU, on your behalf. It is something done TO YOU, not something that you get for yourself. The Kohen HaGadol gets atonement for you. You just need to stay back, shabbat (stop), and deny yourself from indulging in your own desires. The Kohen is the one who then does the cleansing work of atoning for the sins which have resulted from you indulging your own desires in the past year.
It is crucial to understand that you cannot be your own Kohen. (The Torah tells us what befell Korah when he tried to be a Kohen!) God called the Kohaniym near, and gave the Kohen HaGadol alone the job of cleansing the people—which means that you cannot cleanse yourself. Our righteous actions are defiled by our sin, rather than our sin being cleansed by our righteous actions (Isa. 64:6, Hag. 2:11-14). If you try to earn your way into God’s presence through your own good actions, you will end up like Nadab and Abihu—destroyed in the consuming fire of His holiness.
We cannot stand before a holy God without the cleansing of His Kohen.
This is why God sent His Messiah, Yeshua, as an eternal Kohen of the order of Melchizedek (Psalm 110:4). He poured out His own life as a guilt offering for us, and bore our iniquities on Himself as the Azazel goat bore the iniquities of the people (Isaiah 53:10-11). And through the shedding of His own innocent blood, He served as our Kohen HaGadol in the heavenly holy places to atone for our souls, not repeatedly every year, but once for all time! In Him, we are cleansed of our sins forever! He removes our sins from us as far as the east is from the west, and our sins are remembered no more (Psa. 103:12, Jer. 31:33).
The work has been done FOR YOU. The Kohen HaGadol has sprinkled the blood of atonement on your behalf. Cleansing of sin is available to everyone. Submit, humble yourself, get out of the way, and accept the atonement which Yeshua so perfectly provides.