The Talmud tractate that is entirely devoted to the laws for Yom Kippur is called Yoma, which means "the Day."
Even among simple folk, it is known as "the Holy Day."
As indicated in the Torah, and expressed in prayer, this day is essentially one of atonement and purification from sin.
The atonement obtained on this Day of Atonement does not result from one's repentance and self-purification but from its nature as a day of pardon and Divine revelation, emanating from God Himself.
The very notion of pardon and atonement contains a conception of reality that transcends the bounds of common rationality.
The recognition that there is pardon for sins means that, in some way, the past can be changed, that acts which were done, which existed in reality, may be considered as not having occurred at all.
Furthermore, the concept of crime and punishment is primarily based upon the assumption that they have a cause-and-effect relationship, and that, as the biblical verse says, "Evil shall slay the wicked" (Psalm 34:21).
Forgiveness, therefore, is not only a change or reversal of the Supreme Law that defines good and evil but a violation of the laws of causality, an elimination and cancellation of the past.
As it is said, "I have carried away your transgressions like a thick cloud, and your sins as a mist" (Isaiah 44:22).
The pardoning of sins is not like removing a stain, which leaves a faint mark, but like a wind dispersing the clouds, leaving no sign of their having been there before.
Forgiveness becomes, then, the actual creation of a new temporal order in which it is as if the sin never existed.
Moreover, it is as though by the very power of repentance "sins have become merits" (Yoma 86b), and the past is rewritten according to another scale of values.
The sages say that repentance preceded the creation of the world, which means that repentance transports a person above and beyond the realities of the created world, with its order of time, forming, as it were, a new creation.
And since Yom Kippur is the day of Divine pardon and forgiveness, it is the revelation of a Supreme Essence that transcends the limits of the whole world.
The commentary on the verse "I, alone, am He who wipes away your transgression for My sake" (Isaiah 43:25) places the words "I, alone" on a higher level than the "I" with which the Ten Commandments begin (Exodus 20:2).
This revelation, which transcends and cuts through the boundaries of the world, is the essence of this day, and its power is defined in the words of the sages as "the very day itself atones" (Yoma 87a).
–Rabbi Adin Steinsaltz
From A Guide to Jewish Prayer by Rabbi Adin Steinsaltz