A sin offering and a guilt offering for a definite sin provide atonement. Death or Yom Kippur provide atonement together with repentance.  [However] repentance [alone] atones for lesser transgressions: for positive commandments and negative commandments. But for the graver [sins], it suspends [punishment] until Yom Kippur comes and provides atonement.

He who says, “I will sin and repent; I will sin and repent,” they do not assist him in achieving repentance.  [If he says] “I will sin and Yom Kippur will provide atonement,” Yom Kippur does not provide atonement.  For sins between man and God, Yom Kippur provides atonement; but for sins between man and his fellow man, Yom Kippur does not provide atonement, until he appeases his fellow man.  This did R' Elazar ben Azariah expound: From all of your sins before God shall you be cleansed —- [from this we derive] for sins between man and God, Yom Kippur provides atonement; but for sins between man and his fellow man, Yom Kippur does not provide atonement, until he appeases his fellow man.  R' Akiva said: Praiseworthy are you, O Israel! Before Whom do you cleanse yourselves? Who cleanses you? Your Father in Heaven! As it is said: And I will sprinkle pure water upon you and you shall be cleansed; and He also says: The mikveh of Israel is Hashem. Just as a mikveh purifies the contaminated, so does the Holy One, Blessed is He, purify Israel.