Hatarat nedarim is annulment of vows. Breaking a promise (normally accepting something upon yourself, not a promise to someone else) is a serious sin, and before the Day of Judgement on Rosh Hashanah (the New Year, tomorrow and Tuesday, starting tonight), we try to be as sin free as possible. The basic premise of hatarat nedarim is that if the vow was taken based on a mistaken presumption, it may be annulled by a halachic court. Since the gravity of the vow hits home when the judgement is almost upon us, we ask for annulment, as we wouldn't have undertaken the promise with the commitment of a vow knowing and understanding the risks of not keeping to it properly. This is fine before the Jewish males of age, who comprise a Beis Din (Halachic court), who hear the request from the petitioner and pronounce his vows nullified.
