Nagging rights are a privelage inadvertantly granted to a girl at the beginning of a relationship. It generally refers to a gentleman's obligation to put up with ridiculous demands and constant irritation (which he would never do under normal circumastances) from a female partner for the good of the relationship.
Somehow, many women manage to retain nagging rights even after a breakup, especially in the case of divorce.
"Dude, how many phone calls did you just ignore from your ex?"
"Who the fuck cares? She ain't got nagging rights no more!"