In civil law the person doing the suing, the person who says they've suffered some wrong or injury is called 'the complainant" (they used to be called 'the plaintiff') That's one 'party'. The person being sued is called 'the defendant" That's the other party.
Sometimes there are other people brought in. For example, the defendant might say that everything wrong was done by some other person, not him.That person blamed can be made a party to the action. They become the "Third Party".