I'm not a sports fan, but I'm pretty sure a "bye" means you don't have to play. I think the reasoning is that the team presumed to be in the lead sits by while the lesser teams eliminate somebody, and then plays the winner. It gives the players a valuable rest period, too.
"Bye" is also used metaphorically in non-sports-related situations. Father, to teenager who has come home at one o'clock in the morning: "You get a bye this time, son, because we weren't clear about what time we expected you home. But don't let it happen again."