More than Absolution from Guilt
The name Yom Kippur means "Day of Atonement"; it is "the culmination of forgiveness and pardon for Israel." 
The Hebrew term for "atonement" - kapparah, implies not only that the sinner will not be punished for his transgressions, but also that the spiritual blemishes caused by sin will be washed away from his soul.
When a person turns to G-d in sincere teshuvah, the process of change can purge, and even transform, the negative spiritual influences generated by sin. 
It is, however, difficult to understand how can this be accomplished by the arrival of Yom Kippur on the calendar.
How can Yom Kippur itself bring about such a dramatic change in a person's being?
The Essence of the Day Atones
This question lies at the heart of a difference of opinion among our Sages. 
Rabbi Yehudah HaNasi maintains that atonement is granted on Yom Kippur whether or not a sinner repents, because "the essence of the day (itzumo shel yom mechaper) atones." 
The majority of the Sages differ with this view, maintaining that Yom Kippur atones only for those who repent. 
However, even those Sages acknowledge the power of "the essence of the day," in their statement that on Yom Kippur we can atone for sins which cannot be completely atoned for on other days. 
The difference between the Sages and Rabbi Yehudah HaNasi, then, is that the Sages maintain that "the essence of the day" can only affect an individual who through teshuvah has opened his heart to its influence. Rabbi Yehudah HaNasi, by contrast, maintains that the influence of "the essence of the day" is so powerful that it atones even without teshuvah.
In order to understand this difference of opinion, we must analyze the nature of "the essence of the day" and how can it bring about an internal change within a person.
Three Levels of Connection
We relate with G-d at three levels. 
The first level of connection is based on a person's Torah observance: his intellect grapples with Torah study, his emotions find expression in the love and fear of G-d, and his potential for activity is actualized in the performance of mitzvos.
The second level of connection is deeper than that which can be achieved through thought or word or deed. This bond surfaces even when the Torah-based connection to G-d has been severed. At this level, though sin may separate a person from G-d, he will be inspired to turn to Him through the potential for teshuvah. 
Finally, there is a level of connection to G-d which stems from the fact that the essence of the Jewish soul is one with the essence of G-d.
This bond is constant.
At all times, our essence "cleaves to You." 
This bond is not the result of our efforts, and consequently, neither our thoughts nor our words nor our deeds can weaken it.
The connection to G-d established through Torah observance is limited by the extent of each individual's religious commitment and actual observance.
Furthermore, since this connection is humanly generated, it is limited, no matter how inspired and complete our observance is.
Even teshuvah - though it results in a deeper connection than that effected by observance - is limited, because it too requires human input: our yearning not to be separated from G-d.
The essential bond we share with G-d, however, does not depend on us at all, coming about instead, because our souls are "an actual part of G-d from above."  At this level of essential connection, there is no existence outside G-dliness, no possibility of separation from G-d, no possibility that the soul be affected by sin.
The very revelation of this level of connection removes the blemishes which sin causes.
This kind of cleansing is a natural process, for the revelation of one's inner bond renews our connection with G-d at all levels.
When, by contrast, one atones for sin through teshuvah, the deeper connection he establishes breaks through the barriers he has created by his past conduct. Revealing one's innate inner bond with G-d is even more powerful: it leaves no possibility of imperfection.
This is the meaning of saying that "the essence of the day atones."
On Yom Kippur, one's essential bond with G-d is revealed, and in the process, every element of our spiritual potential is revitalized. 
Locked In, Alone With G-d
The revelation of this essential bond on Yom Kippur is reflected in the High Priest's entry into the Holy of Holies, during which he came into direct contact with the Divine Presence. No human or spiritual being  was permitted to intrude upon his connection with G-d.
This same degree of connection can be achieved by each of us through our divine service on Yom Kippur, and in particular, during the concluding Neilah service.
Neilah means "closing" or "locking".
At this time, every individual Jew is locked in, alone with G-d.
At this time, the essence of his soul, the level that is one with the essence of G-d, is revealed.
Neilah is the fifth prayer service of Yom Kippur.
Our Sages explain  that there are five levels within the soul.
The fifth and deepest is called yechidah, from the word yachid which means "singular oneness."
This is the point in the soul that is united in singular oneness with G-d; this is the level that surfaces during Neilah. 
The level of soul experienced during Neilah foreshadows the Era of the Redemption, for Mashiach represents the yechidah of all existence  and will reveal this unique connection in every aspect of our being.
May this take place in the immediate future.
- Neilah liturgy; Rambam, Mishneh Torah, Hilchos Teshuvah 2:7.
- See the previous essays entitled "Teshuvah - Return, not Repentance" and "Transforming Evil."
- Shavuos 13a.
- Toras Kohanim, commenting on Vayikra 16:30.
- This opinion is accepted as halachah (Rambam, loc. cit. 1:3, Hilchos Shegagos 3:10; Shulchan Aruch HaRav 607:16).
- Yoma 86a; Rambam, Hilchos Teshuvah 1:3-4. Significantly, though the Rambam follows the opinion of the Sages, in the above halachos he quotes the expression, "the essence of the day atones."
- See the above essay entitled "At One with the King."
- Similarly, this inner potential inspires a person who has not sinned to achieve a more powerful relationship with G-d.
- The Hoshanos prayers of the third day of Sukkos.
- Iyov 31:2, as paraphrased in Tanya, ch. 2.
- As explained in Note 8 to the above essay entitled "At One with the King," both Rosh HaShanah and Yom Kippur express an essential level of G-dliness that transcends their more general function as "days of teshuvah."
- Jerusalem Talmud, Yoma 1:5.
- Bereishis Rabbah 14:9; Etz Chayim, Shaar 42, chs. 1-2. On the Essence of the Teachings of Chassidus (Kehot, N.Y., 5738) explains these five levels at length.
- Likkutei Torah, Parshas Pinchas, p. 86b.
- See the gloss of the Ramaz to Zohar II, 40b. See also On the Essence of the Teachings of Chassidus.