Prejudice means “pre-judging” something. In general, it implies coming to a judgement on the subject based on false beliefs or before knowing where the preponderance of the evidence actually lies. Prejudice may involve discriminatory attitudes of individuals toward people or things or impairment to the rights of a party in a legal dispute.
The phrase “without prejudice” means that a claim, lawsuit, or proceeding has been brought to a temporary end but that no legal rights or privileges have been determined, waived, or lost by the result. For example, if a party brings a lawsuit in small claims court but discovers that the claim is over the amount for that court to have jurisdiction, the lawsuit can be dismissed “without prejudice”. This means that the dismissal is no bar to bringing a new lawsuit in a court that does have jurisdiction.
By contrast with prejudice means that a party’s legal rights have in fact been determined and lost. To continue the same example, if instead the court had jurisdiction, but the plaintiff did not appear for the trial, the court would dismiss the case “with prejudice”. That dismissal is a judgment against the plaintiff “on the merits” of the case, and extinguishes the claim that was being sued over. However, this does not prevent an appeal or a trial de novo if ordered by a higher court.