During the month of Elul, prior to Rosh Hashanah and Yom Kippur, we prepare to seek forgiveness.
Forgiveness is divided into two distinct varieties: forgiveness from God and forgiveness from other people. These reflect the two basic types of mitzvot / commandments that we may have, shall we say, missed out on:
1. Mitzvot bein adam la-Maqom / mitzvot that relate to God
2. Mitzvot bein adam le-havero / mitzvot that relate to others
God can forgive us for those transgressions in the first category; that's what Yom Kippur is for. We atone for times when we have failed to meet God's expectations, but do not affect our relationships with others, like violating the principles of Shabbat or kashrut (dietary laws).
But God cannot forgive us for those ways in which we have mis-handled our obligations to others, like being deceitful or judging others unfairly or spreading gossip. To achieve forgiveness for these transgressions, we must ask the person whom we have wronged.