The Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204), in the first chapter of his Hilchot Teshuba (listen to audio recording for precise citation), discusses the crucial role played by the "Se’ir Ha’mishtale’ah" in achieving atonement on Yom Kippur. The ""Se’ir Ha’mishtale’ah" was the goat which would be sent out into the desert on Yom Kippur and cast off a cliff, whereby it would atone for all the nation’s sins. The Rambam stresses that the goat would atone for all sins committed by Beneh Yisrael, including both intentional and inadvertent sins, and even for sins of which the perpetrator was entirely unaware. The Kohen Gadol would therefore declare Vidui (confession) upon the goat, confessing all the nation’s sins, before sending the goat into the wilderness.
However, the Rambam adds, the "Se’ir Ha’mishtale’ah" earned atonement only for those who repented. For those who did not repent on Yom Kippur, the goat earned atonement only for the "Kalot," or "minor" transgressions. This includes all violations except for offenses punishable by death or Karet (eternal spiritual excision), such as Shabbat desecration and eating Hametz on Pesah, and the sin of uttering a false or unnecessary oath. These especially grievous sins cannot be atoned even through the "Se’ir Ha’mishtale’ah" unless the sinner repents.
In the absence of the Bet Ha’mikdash, the Rambam writes, when we do not offer sacrifices or perform the "Se’ir Ha’mishtale’ah" ritual, our only means of earning forgiveness is repentance. Teshuba (repentance) has the capacity to atone for all sins, even if a person lived as a sinner his entire life and repented just before his death.
However, the Rambam adds, different kinds of sins have different requirements for atonement. If a person neglected to perform a Misvat Aseh (affirmative command), such as if he neglected to take the four species on Succot, then he earns atonement immediately once he repents and confesses. If a person violates a Misvat Lo Ta’aseh (Biblical prohibition) which is not punishable by execution or Karet, such as if he wore a garment made from Shaatnez, then his atonement is held in abeyance until Yom Kippur. He earns atonement through Teshuba and Yom Kippur, but not through Teshuba alone.
The next category is capital offenses – sins that are punishable through court execution or Karet. For these violations, full atonement is achieved only through the combination of Teshuba, Yom Kippur, and Yisurin (afflictions, or punishment). Even after one repents and Yom Kippur passes, the violator does not achieve atonement until he endures some sort of suffering, Heaven forbid.
The final and most grievous category of sin is that of "Hilul Hashem" – sins which caused God’s Name to be disgraced. The Rambam writes that a person who commits a sin of this kind is not completely forgiven until he dies. Even after Teshuba, Yom Kippur, and suffering, his sin remains on his record until death.
Summary: The means for achieving complete atonement for a sin depends upon the gravity of the sin. Some sins are atoned immediately once the person repents, while others require both repentance and Yom Kippur. Especially grievous sins are atoned only through Teshuba, Yom Kippur and suffering, and sins that cause God’s Name to be defiled are not fully atoned until the perpetrator dies. In any event, repentance is an indispensable prerequisite for achieving atonement for any sin a person commits.
