Judge Judy is a real court, and the people appearing on the show are real individuals with actual disputes. They are not actors, and the cases are genuine. The show is filmed in a real courtroom setting, and the judgments issued by Judge Judy are legally binding.
The participants in the show are chosen from a pool of people who have filed small claims lawsuits in various jurisdictions. They agree to appear on the show and have their case heard by Judge Judy, who acts as an arbitrator.