Refers to situations in which only one party (and not the adversary) appears before a judge. Such meetings are often forbidden.
Although a judge is normally required to meet with all parties in a case and not with just one, there are circumstances where this rule does not apply and the judge is allowed to meet with just one side (ex parte) such as where a plaintiff requests an order (say to extend time for service of a summons) or dismissal before the answer or appearance of the defendant(s).
In addition, sometimes judges will issue temporary orders ex parte (that is, based on one party's request without hearing from the other side) when time is limited or it would do no apparent good to hear the other side of the dispute. For example, if a wife claims domestic violence, a court may immediately issue an ex parte order telling her husband to stay away. Once he's out of the house, the court holds a hearing, where he can tell his side and the court can decide whether the ex parte order should be made permanent.