In American football, a "bye" is when a team does not have a game during a given week in the course of the regular season. The NFL uses byes to extend the regular season to 17 weeks. Bye weeks typically occur between the fourth and 12th week of the season.
The bye has a slightly different function in other sports. In tournaments, a bye signals that a competitor does not have an opponent in a particular round of the competition and automatically advances to the next round. The use of byes in a tournament allows it to run smoothly, even if there is not an ideal number of competitors for that type of tournament.