"To hear the case" means to listen and consider all the facts, arguments, and evidence presented for a particular legal dispute or issue in order to make a decision or judgment on it. Full definition
The criminal courts hear cases where the State has filed charges against one or more persons alleged to have committed criminal offenses. (lacourt.org)
Once appointed, appellate judges begin hearing cases in appellate court. (thebalancecareers.com)
And it has often heard cases on controversial subjects years before Canadian courts have tackled them. (slaw.ca)