Asking for forgiveness
Another essential Jewish practice associated with this time of the year is asking forgiveness of those whom one may have wronged. Essential, because as the Mishnah teaches, Yom Kippur only atones for sins between people and God; those between people are only forgiven after we have asked forgiveness from whoever we wronged (Talmud Yoma 85b).
It is necessary, of course, also to repay money that we may have gained improperly, but even that does not discharge our indebtedness to the other person until we actually say we are sorry (Maimonides, Hilchot Teshuvah, 2:9).
It is easy to piously ask for forgiveness from people whom we have harmed in trivial ways if at all, but harder to get up the courage to approach people whom we know we have really wronged. There is an interesting halachic disagreement about whether it is necessary to ask forgiveness for something that the other person does not know you did to them (say you slandered them behind their back, for example). On the one hand, you require their forgiveness. On the other, maybe they will be hurt more by finding out what you did. If you're in this situation, ask a rabbi...