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If you lose some money or cut your finger, someone might say to you in a comforting tone, "It should be a kapparah." They would mean by this that they hope the annoying, but relatively minor loss or damage will offset and so avoid the occurrence of something worse.
The word itself comes from the verb kiper, meaning to cover or ignore. (It can also mean to deny; one who is "kafar b'ikar" denies the existence of God.) From this kapparah comes to mean "expiation;" something that wipes out or erases guilt or sin.
The Eve of Yom Kippur in Meah Shearim, Jerusalem is marked by the picturesque ritual of kapparot. A cock is taken, swung around the head three times while the penitent declares "this is my kapparah, with the idea that any looming misfortune as a result of sin somehow be transferred to the animal. Some rabbinical authorities have denounced kapparot as a heathen superstition (Rabbi Yosef Karo called it a "stupid custom".) The ritual endures through its raw emotional power.
Yom Kippur is the day of kapparah. We are responsible to for doing teshuvah; making an account of our deeds, regretting our past sins and sincerely resolving to do better. Kapparah, however, is beyond our control. This is the grace through which God erases the memory and the consequences of sin in the merit of our teshuvah and observance of Yom Kippur.