Adversarial systems are where two advocates represent each side and attempt to convince an impartial third party (a jury, a judge) of their case. The court is an impartial referee between the two sides. This is the legal system in most common law countries (e.g. the United Kingdom, areas of the Commonwealth, etc.). In this system, the court isn't involved in investigating the facts of the case: that's up to the advocates.

This is in contrast to the inquisitorial system used in civil law countries (e.g. France, Italy) where the court is actively involved in establishing the facts of the case - so they're not an impartial referee like they are in the adversial system.