A duel is a fight between two people, usually using swords or other weapons. If you tend to be a little cowardly, you're probably glad that people aren't expected to defend their honor with a duel these days.
The classic definition of a duel is the kind that happens all the time in Shakespeare plays: two men clanking swords together in a battle to the death over some issue of honor or betrayal. Today, the word duel can be used to talk about any kind of contest or struggle — like a duel between political candidates. The word duel can be traced back to both duo, Latin for "two," and also duellum, which means "war."