Immediately after kol nidrei we recite the pasuk,"V'nislach l'chol adas Bnei Yisrael... ki l'chol ha'am b'shegagah." Asks the Sefas Emes: how can we say this when we know it's not true? Shegagah means a sin done unwittingly. I don't know about you, but certainly some of my aveiros were things I did even though I knew they were wrong!
Chazal tell us that if someone does teshuvah m'ahavah their sins become zechuyos; if someone does teshuvah m'yirah, sins done intentionally count only as a shogeg. It is impossible, explains the Sefas Emes, for a person to come to Yom Kippur and not feel a stirring of at least a little teshuvah m'yirah inside. When you sinned, it may have been intentional, but once Yom Kippur comes, teshuvah comes and knocks those sins down to at least just a shogeg.
One of my kids asked why we say "slach lanu..." in ma'ariv after Yom Kippur. We've all heard the answer of the ba'alei mussar that we've already started thinking about what to eat and do after the fast during ne'ila and need forgiveness for that. But the Chiddushei haRI"M answers that the reason we say "slach lanu" is because we fail to completely believe in the power of Yom Kippur. Once we've reached the climatic moment of ne'ila there is no question that Hashem has heard our tefilos and forgiven each and every one of us and we have a clean slate. But how many of us really feel and believe that? How many of us walk out of ma'ariv feeling 100% like a "biryah chadasha" with no baggage of the past? And so we have to say "slach lanu..."
The Sefes Emes explains that "m'erev ad erev" hints to "ta'aroves," mixture. Yom Kippur is not just one special day set apart from the rest of life -- we have to mix the aliya of Yom Kippur into every day and make it part of the rest of the year.