According to tradition, on the first day of the month of Elul, Moses ascended to Mount Sinai, after having broken the first tablets due to the sin of the Golden Calf. Forty days later, on Yom Kippur, he descended with the second tablets. At that point, Yom Kippur became a day of atonement and absolution for iniquity.

Ben Beteira says: Moses remained forty days on the mountain, expounding words of Torah and analyzing its letters. After forty days he took the Torah and descended on the tenth of the seventh month, on Yom Kippur, and he bequeathed the Torah to Israel as an eternal statute, as it is stated: “This shall be an eternal statute for you” (Leviticus 16:34).

Were it not for Yom Kippur the world would not survive, as Yom Kippur atones in this world and in the World to Come…. Even if all the festivals are abrogated, Yom Kippur will not be abrogated, because Yom Kippur atones for minor and major transgressions, as it is stated: “For on this day he shall atone for you, to purify you from all your sins” (Leviticus 16:30). It is not written: “From your sins,” but rather, “from all your sins.” (Pirkei deRav Eliezer 47)