Yom Kippur is the day that atones for the sins of the Jewish people. The word Kippur comes from the word kapra, which means atonement. How does atonement work, and what does the concept of atoning for a sin mean? In the Talmud (Shvuot 13a), there is a discussion about the function of Yom Kippur atonement: according to the opinion of Rabbi Yehuda HaNasi (Rebbi), the essence of the day is to atone for sins, while according to the opinion of our sages (Rabanan), Yom Kippur is a day of atonement only for those who do Teshuvah (repentance).
Analyzing the opinions presented in detail, it becomes clear that the discussion is not about whether the inherent holiness of the day atones for sins, but rather about how each Jew can attain the atonement that the day itself provides. According to Rabbi, it is enough for the day to arrive, and it alone effects the atonement for sins. According to Rabbanan, it is necessary for the person to perform Teshuvah (repentance for the past and resolve for the future) for the atonement that the day itself, given its holiness, achieves to take effect.
The concept of atonement not only means that the person will not be punished for the sin committed, but, from a deeper perspective, the idea of atonement is about cleansing the defect and stain inflicted on the soul through sin.
When a person transgresses the Divine Will (the 613 commandments), they create a defect in their soul and in the heavens. To correct this defect, they must access a spiritual level higher than the Divine Will itself (the source of the commandments). In other words, to repair the damage done at a given level, one must access a higher level to draw upon the energy necessary to correct the lower level. This is the concept of Teshuvah (repentance).
In the union between a Jew and God, there are three general levels: 1) the union achieved through the observance of mitzvot (commandments). This level implies that the Jew accepts the heavenly yoke upon himself, fulfilling the Divine decrees. 2) a deeper union, which is expressed in the fact that even when one has transgressed the Divine Will, having removed the heavenly yoke, one still feels troubled, feels bad, and performs Teshuvah (repentance). The very fact that Teshuvah comes from a higher level than the observance of mitzvot gives it the power to correct the defect caused by the failure to fulfill them. However, this level is limited by the depth of each individual's Teshuvah. 3) the essential union existing between the Jew and God, an unlimited union, which is not expressed in any particular way, neither through the observance of the precepts, nor through Teshuvah, but is part of the nature of the Jew, who is a piece of God indeed.
This ultimate level of union between God and the Jew, just as it cannot be created through human service, due to human limitations, also cannot be destroyed by any human action, not even those contrary to the Divine Will. At every level of union where sins have an effect, the Jew must perform Teshuvah (repentance) to create a new connection that replaces and corrects the previous one. However, at a level where sins "do not reach"—that is, where the Jew's actions have no effect—there is no need for Teshuvah to repair the connection, because it was never affected!.
On Yom Kippur, this level of union is revealed, and that is why the Talmud says that the essence of the day atones. Since on this special day the essential union between the Jew and God is revealed, a union that transcends all actions, it has the power to correct all kinds of defects caused by the Jew's actions throughout the year.
The only difference between the opinions of Rebi (that Yom Kippur is atoning without Teshuvah) and Rabanan (that Yom Kippur is atoning only with Teshuvah) is that, according to Rabanan, Teshuvah is necessary to reveal in the penitent's heart this level of union that Yom Kippur itself expresses. Both agree on the meaning of Yom Kippur, on the concept of the essential and eternal connection between the Jew and God; the discussion lies in whether Teshuvah is necessary for each person to be able to feel with their heart the connection or not.
Halakha (Jewish law) is like Rabbanan.
Extracted from Likutei Sichot vol 4, p. 1149