Someone guilty of infidelity is cheating on a spouse or romantic partner. A common cause of divorce and heartbreak is infidelity.
Fidel means "faithful" or "loyal." Tack on the prefix in, which means "not," and you've got yourself infidelity — the act of being unfaithful. The word can also be used to refer to someone's religious beliefs. Run angrily through a church and claim that God doesn't exist, and your fellow churchgoers will think you lack faith, or that you are guilty of infidelity.