A court is a room where justice is administered. Many popular television shows feature scenes in court, although it’s debatable whether these depictions are realistic.
Court can refer not just to the courtroom but also to the judges who preside over it, as in the example of the U.S. Supreme Court. Court can also refer to monarchs and their attendants, as in the phrase "royal court." As a verb, court means “try to win the affections of someone,” as, historically, people sought to win the favor of royalty. (But if you try courting anyone in a modern courtroom, you'll probably be accused of bribery.)