A duel is a fight between two people, usually with swords or guns. It's often thought of as a formal and serious contest.
Dueling used to be more common than it is now, but back then it was seen as an honorable way for gentlemen to settle their disputes or defend their honor. In those days, if someone insulted you or made a challenge, you might take them up on the duel. If you were a noble or a wealthy person, dueling was considered acceptable behavior. Today, of course, most people would never engage in something like that, and in many countries it's even against the law.
Arranged, regular combat between two private persons, often over a matter of honor.
To engage in a battle.
