With prejudice is a legal classification of a case that has reached a determination; it means that the court is satisfied that there is no basis for the plaintiff's case and that the plaintiff will not be able to take a new case against the defendant on the matter. In effect, the court feels that the legal matter is resolved or that a cause of action does not exist. In any case, the judge can make the ruling that there is not enough evidence to further the case at that moment in time. When a case is dismissed with prejudice, it means that the matter is over and that the plaintiff cannot bring the same cause of action against the same defendant back to the court.
The differentiation between with or without prejudice is made so that spurious cases cannot be tried twice in different ways. It is also a follow-on from the U.S. Bill of Rights, which forbids a court from trying the same person twice for the same crime.