The translation of Yom Kippur is Day of Atonement. The word atonement implies cleansing, since the lack of observance of the Torah's precepts generates a certain spiritual impurity that must be cleansed.
However, it is not "free." Our sages explain that in the universe, the only thing that is immediately and freely available is impurity (it is worth noting, though not elaborating on this now, that we live in a society whose foundation is immediate and easy gratification of any kind... the very definition of impurity...). Regarding these special days from Rosh Hashanah to Yom Kippur inclusive, this "cleansing" occurs through three components that are generally misunderstood: teshuvah (repentance), tefillah (prayer), and tzedakah (charity).
Teshuvah
The world translates this word as repentance. It is true, it is an essential component for cleansing the past and improving the future; however, the deeper meaning of this word is return. The motivation for cleansing on Yom Kippur is the return to our own source, to God. There may be people who have nothing to repent of, either because they have no negative actions or because they don't even know what their obligations and rights are under the Torah, but there is no human being who cannot grow closer to God.
Tefillah
The world translates it as prayer. Man prays to God, praises Him, asks of Him, and thanks Him. And God, when He wills, answers and fulfills the requests. This system works, but there is something more. Tefillah implies the union of Man with God. It is not enough to simply approach God; there must be a union that creates a channel for the transmission of life and energy between God and Man, and that is Tefillah.
Tzedakah
The world interprets charity as meaning there is a rich person and a poor person, and the rich person helps the poor person. From a Jewish perspective, Tzedakah is justice, where the rich person uses the money God entrusted to them to manage wisely and gives a portion of it to the poor person.
Only when Man draws near to God (Teshuvah), can he feel the good and necessary nature of being connected to Him (Tefilah) and bring to practical and daily life, spreading throughout the entire universe that imminent presence of God in all things (Tzedakah).
May it be God's will that, just as it was at the inauguration of the First Temple, in the time of King Solomon, that the Jewish people celebrated the event to such an extent that they continued eating on Yom Kippur and it was approved in heaven, that this year we may celebrate Yom Kippur in the Third Temple, in Jerusalem, in the Land of Israel, with Messiah, Amen.
Gmar Jatimá Tová - May you have a good sealing end