Based on a Naaleh.com shiur by Rabbi Michael Taubes
In the Torah, Yom Kippur is referred to in the plural form as Yom Hakippurim. Rav Soloveitchik explains that atonement is associated with sacrifices, which were a major part of the Yom Kippur service. The Rambam writes that since today there are no sacrifices, teshuva atones for all of our sins. Referring to Yom Kippur in the singular might lead us to think that we cannot attain atonement today because we don’t have korbanot. Therefore, it is referred to as Yom Hakippurim
Every person approaches teshuva with his particular background. There’s repenting from fear and repenting from love. A person can do teshuva while he is still young or when he reaches old age. Therefore we say, Yom Hakippurim to allude to the many different types of teshuva and the varied levels of atonement. Another reason for the plural form is that Yom Hakippurim also applies to atonement for the dead and the living. In fact, the practice to recite Yizkor was originally associated with Yom Kippur. The dead, whose judgment is ongoing, achieve atonement on Yom Kippur too.
In the Torah, vidui is discussed in the context of korbanot. It is not mentioned in relation to Yom Kippur. During the times of the beit hamikdash, the procedure a person underwent to purify himself literally transformed him into a new being. This is the essence of Yom Kippur. A Jew must become a different person to the point where he can say to Hashem, “The decree you placed upon me doesn’t apply anymore.” This encapsulates the concepts of teshuva and tahara (purification). The idea of mechila (forgiveness) has its roots in monetary law where a person can forgive a liability. Similarly, we ask Hashem to overlook our debt of sin. When a person purifies himself it’s as though his sins are completely erased. In the Yom Kippur prayers, we say, “Ki bayom hazeh yichaper aleichem l’taher etchem.” The essence of Yom Kippur is purification and the power of the day itself brings atonement, even without korbonot. According to one opinion the atonement comes even without teshuva. That is why there is such joy on Yom Kippur, and especially at its culmination.
Our sages tell us that when a person does teshuva out of love, “z’donot naasu lo k’zechuyot,” his intentional sins becomes merits. How do we understand this?
We become a different being when we repent. The same energy and creativity that we invested in sin is now put into mitzvot
Selichot are prayers of forgiveness. The central motif is the recitation of the thirteen attributes, which appears numerous times throughout Neila. If we want to be the beneficiaries of Hashem‘s chesed we must live up to these attributes. We don’t recite the full vidui during Neila. This is because we’ve already confessed our specific sins throughout the day. Yom Kippur is supposed to lead us to something beyond this, to a place where our focus turns to our central mission in life and our true goals.