Law.com defines "ex parte" as a motion, order or hearing granted for the benefit of only one party. This is a counteraction to the common court procedure of both parties being required to be present to argue each side of a case. The term is Latin for "one party."
Law.com states that ex parte usually serves as a precursor to a formal hearing and often results in a request for a continuance.
About.com states that ex parte orders are usually related to child abuse and domestic violence situations. In many of these cases, restraining orders are administered during such trials that stand until the official trial.