Nonmovant means the non-moving party.

When a party asks a judge to do something (issue a ruling or other decision), it is called a motion.  For example, a defendant could move the court to dismiss a case for lack of personal jurisdiction. In this case, the defendant, who is making the motion, is called the movant, or moving party.  The plaintiff (who will oppose the motion to dismiss), is called the nonmovant, non-moving party.