To adjudicate is to act like a judge. A judge might adjudicate a case in court, and you may have to adjudicate in the local talent show.
Do you see a similarity between judge and adjudicate? When you add the common Latin prefix ad meaning "to" or "toward," you have a pretty good idea what the word means. But a judge isn't the only person who can adjudicate. If you're fighting with your little brother or sister and make them cry, your parents may adjudicate and send you to your room.