This is a term used in college athletics, including football, which describes a mechanism by which a student-athlete is able to practice with a team and attend classes while not using one of their four years of athletic eligibility. There are other reasons, such as medical issues, for a player to skip an entire year of competition. The term could be used to describe the action of a coach using this mechanism, or to describe or identify the player. For example, a coach may "redshirt," a freshman who is then called a "redshirt freshman," or simply as "a redshirt."
This mechanism was created in order to allow young men and women student-athletes to jump-start their academic careers while taking their athletic careers more slowly. This allows the players to practice with the team, learn the playbook, and get to know teammates before being required to play. This gives the players a chance to develop both physically and mentally, which helps the coach build the team. By extending their four years of athletic eligibility across as many as five or six years, coaches are able to spend more time with the athlete; developing, teaching, and hopefully, helping the athlete contribute to wins on the field. The term comes from the color of the jersey these players typically wear while practicing with the regular players.