The NFL bye week is a mechanism built into the football schedule in order to give teams a rest approximately midway through the season. The earliest bye week is usually Week 4, and teams can have a bye week all the way to Week 12. The NFL tries to alternate teams having an early vs later bye week. Additionally, the NFL likes to give a team a bye week if they are playing an international game in order to allow the team to adjust.
The bye week is very helpful to players as it gives their bodies a chance to rest and come back ready for football. Teams that have had many player injuries are also given a chance to bring these players to full health for the remainder of the season. The bye week can be a negative however if a team has a bye week between Monday and Thursday night games as they have less time, although the NFL tries to avoid scheduling situations such as these.
Teams can handle the bye week differently. Some teams still want their players around the facility in order to continue practicing lightly or making sure they are doing the proper exercises to heal. Other teams basically treat the bye week as a vacation time, allowing players to head home for a few days in order to spend time with family and friends, time that players normally do not get during the regular season.