A bullpen game is exactly how it sounds. Instead of going with a traditional starter, who will go 5-6 innings before turning it over to the bullpen, a reliever starts the game. That reliever pitches an inning, maybe two, and then it becomes a chess match. The managers are trying to confuse each other into getting the best matchups. It’s something you rarely see in the regular season, mostly because teams will always have a five-man rotation, no matter what.
However, it happens frequently in the playoffs, especially closer to the World Series. Most teams only bring three true starting pitchers in the postseason, which means that in a seven-game series, game four usually turns into a bullpen game.