Also a
sports term for when a
team or teams do not have to play a
game while other teams do.
Byes usually take place in two possible ways: postseason tournaments, and natural byes due to the schedule.
In the former case, if a tournament has a number of teams other than a power of two, then every team can't play at once (ie. if there's 8 teams then there would be four matches, but if there's 9 there'd be one team left out). Different conferences and leagues have various ways to work this out.
For example, in NFL football, each conference has 6 playoff teams. The bottom four play in the wild card round, with the two winners advancing to the conference semifinals to face the top two teams which had byes (so did not play during the wild card round). In other words, teams ranked 3-6 play each other, with the two winners facing teams ranked 1 and 2.
Various combinations allow for a tournament with most any number of teams. For example, with 5 teams, the bottom two teams play in the first round, while the top 3 teams receive a bye to the semifinals. 11 teams would involve teams ranked 6-11 playing, with the 3 winners joining the top 5 teams (who were on bye) in the quarterfinals.
Obviously, such byes aren't only for sports. They can also be used in chess tournaments or video game tournaments, or any head-to-head competition.
The second sort of bye is a "natural" bye. For example, in the NFL, all teams play 16 regular season games. However, they play over 17 weeks. So each team has a bye week in their schedule, during which they have no game. Generally, this sort of bye is only for "bye weeks". When baseball teams have the day off, or a hockey or basketball team doesn't play for several days, they are never really said to be on bye.