When people get accused, there will be a trial. Usually, the trial is there to see if the person is guilty, and if this is the case, what the punishment should be. A show trial is different: the question whether the person is guilty (called a verdict) has been made before. The trial is held so that accusations and the verdict can be presented to the public, serving as an example and a warning to other would-be dissidents or transgressors.
Show trials tend to be retributive rather than corrective, and they are also conducted for propagandistic purposes. When aimed at individuals on the basis of protected classes or characteristics, show trials are examples of political persecution. The term was first recorded in 1928.
A similar concept is "kangaroo court".