...In the seventh month, on the tenth day of the month, you shall afflict your souls, and you shall not do any work ... For on that day he shall provide atonement for you to cleanse you from all your sins before the LORD. - Leviticus 16:29-30
Though wary of over-simplification, let me sum by saying that Yom Kippur atones only for those sins committed against God, not for sins committed against another person, as Jews believe those must be atoned for first by going directly to the person they have wronged. And, let me add that Yom Kippur begs a truth, which is that to participate one must believe that sins have been committed. And this, of course, begs the question: what has happened to this notion in our culture today? As it appears we are at risk of thinking this is not so based upon our actions and heart. Still... Jews across the world will today so observe, and we Christians, of course, follow the same in our theology. We believe that our sins - all sins - are in need of being atoned for, meaning their penalty paid and forgiven; and that the only way this can be done is by the provision given by God Himself, which is His Son and our Savior, Jesus Christ.
Yes, the Bible makes it clear that sin - both toward our fellow man and God - is real. It also is clear that God is just, and that, as a just God, He cannot and will not tolerate sin un-atoned. But thanks be to God that, by His grace, there is a way just as the prophet Isaiah makes clear:
All we like sheep have gone astray, we have turned everyone to his own way, but God has laid on Him the iniquity of us all. Isaiah 53:6. .
For I believe that the "Him" of Isaiah's verse is Christ - that Yom Kippur has come - and now really is a blessed day...