This is a baseball phrase which refers to a game in which the two starting pitchers, or two active pitchers, are consistently and continuously get batters without many or any runs being scored on either side. The game is illustrated by lots of strikeouts, few hits, few runs, and few pitches pitched by either pitcher. Although it will typically involve starting pitchers, a pitcher's duel can start late in the game if two relief pitchers come in.
The term pitcher's duel comes from the fact that there is only one pitcher active in the game, and if they are the only ones producing outs for their team, they are essentially playing each other. A duel is defined as a competition in which there are only two main competitors. This is precisely the case in such a game. Although it cannot be predicted who will produce what could be known a pitcher's duel, all-star pitchers or pitchers who have previously won an MVP or Cy Young Award typically produce such a game.