"A man or a woman who sins... let them confess their sins."
One is required to repent and confess his sins, to feel regret and shame
over his wrongdoings, and to commit himself to improve his ways. This
mitzvah applies all year, but Yom Kippur is our last chance before the
final judgment of the year.
By verbally admitting that we have sinned, we are acknowledging that
1. We understand that Hashem knows everything we do;
2. We are sincere in our regret; and
3. We will try harder next time to refrain from this sin.
Thus, Hashem will forgive us and help us to improve (Sefer
HaChinuch, mitzvah 364).