A duel is a 1 on 1 Battle or Capture The Flag match. Most duels happen during JDC and JJ2WC.
Duels have not always been important in the community. They were popularised by the aforementioned JDC.
Most people duel until someone has 10 points. The first person who reaches that score wins, although 5 point duels have also become quite popular, since duels last for less time, and there is much less room for error, thus increasing the pressure.
Eat your lima beans, Johnny.