Each player plays other players who have done as well (or poorly) as themself. Each player has a score that increases when they win. The player with the highest score at the end of the tournament wins.
Swiss format is also called Winners-Play-Winners.
Players receive a starting score of 0, and are paired up at random for their first game. Winning players have their scores increased by 1. Then players with the same (or similar) scores are paired up at random for subsequent games. However, no player is ever paired up with the same player twice.