It's one of a whole bunch of "real-life court case" shows, which have sprouted up ever since the popularity in the 80s of Judge Wapner's The People's Court. Judge Judy seems to have more of an attitude than most of those TV judges. Generally, on such shows, all participants are paid an appearance fee, to which amounts of judgments are added or subtracted as appropriate, so questions of legal bindingness needn't come up except with regard to whatever contract terms the participants may have to agree to prior to the appearance (of which I know nothing, having not actually seen their contract).