The adjective appellate is good for talking about the legal process for hearing appeals. An appellate court of law mainly deals with people attempting to reverse legal decisions.
After a defendant has been convicted of a crime, she has the opportunity to appeal that decision, or apply to have her case re-tried. The judge who would hear this new case is called an appellate judge, and the court in which the case would be heard is an appellate court. The word appellate is a legal way to say "relating to appeals," and its root is the Latin appellare, "to address, appeal to, or summon."