The meaning of the name Yom Kippur:
What is the essence of Yom Kippur, its inner meaning and purpose? A name reveals the essence of an item. Yom Kippur is the day we receive atonement from Hashem for our sins. It however remains to be understood why one receives this atonement specifically on Yom Kippur? Isn’t atonement achieved through Teshuvah [repentance] which is a Mitzvah to perform any time of the year in the event of sin? What distinguishes Yom Kippur from the regular performance of Teshuvah during the year? One could possibly answer that although Hashem always accepts Teshuvah, Yom Kippur is the only day of the year specially designated just for Teshuvah. However, if this were the case, then the Holiday should be called Yom Teshuvah rather than Yom Kippur. From the fact it is called Yom Kippur, it is implied that there’s a special atonement which only occurs on Yom Kippur which even surpasses the atonement derived through Teshuvah.
Is Teshuvah required on Yom Kippur in order to receive atonement?
The Gemara in Shavuos brings an argument between Reb Yehuda and Chochamim. Rebbe Yehuda holds that the essence of the day of Yom Kippur atones for a person’s sins even without him doing Teshuvah. The Chochamim hold one must do Teshuvah in order to merit receiving the day’s atonement. The final ruling in Halacha sides with the Chochamim. According to both opinions however, it is the day of Yom Kippur itself which atones, the argument is only with regards to if one must do Teshuvah on this day to merit its atonement. What is the meaning of this? How can a day atone? How can one receive atonement without doing Teshuvah?
The essence of a Jews soul is free from sin-Teshuvah reveals the essences:
The Chassidic teachings explain that the Jewish soul is an actual part of G-d above which contains five levels. The lowest level relates to action, the second to emotion, the third to intellect, the fourth to will, and the fifth is the essence of the soul. The first four levels, being that they are not the essence, have a weaker unity with its source, which is Hashem. In order to be fully united with Hashem, they require fulfilling the will of Hashem, which are the Mitzvos found in the Torah. Due to this, these four levels become affected by sin, becoming blemished and stained through sin, making it cause a separation in its unity with Hashem. However, the essence of the soul is absolutely one with G-d Himself, even without fulfillment of the laws of the Torah, and just as one cannot affect or blemish G-d through sin, so too this part of the soul cannot be affected by sin. On Yom Kippur, it is this part of the soul that is revealed; the essence of a Jew which is one with Hashem and immune to all obstacles threatening separation from its source. This revelation thus cleanses the other aspects of the soul, removing from it all of its blemishes caused by sin, and reuniting it with its source. However, as mentioned before, according to the final law, one is required to repent to merit this revelation. For this reason, the prayers of Yom Kippur are filled with confessions, as this is a part of Teshuvah. According to the above, Yom Kippur doesn’t mean “The day of atonement” but rather “The day is atonement,” as it is the day itself which atones.
 Likkutei Sichos 4 p. 1149; 27 p. 124; See also See Melukat 4 p. 17
 Shavuos 12b
 Rambam Hilchos Teshuvah 1:2-3; Likkutei Sichos ibid
 Likkutei Sichos 4 ibid
 Likkutei Sichos 4 p. 1149; 27 p. 124