To repudiate something is to reject it, or to refuse to accept or support it. If you grow up religious, but repudiate all organized religion as an adult, you might start spending holidays at the movies, or just going to work.
This verb usually refers to rejecting something that has authority, such as a legal contract, doctrine, or claim. In connection with debts or other obligations, repudiate is used in the specialized sense "to refuse to recognize or pay." If referring to a child or a lover, repudiate is used in the sense "to disown, cast off." This verb is derived from Latin repudiare "to put away, divorce."