This comes right off the NCAA website:
The term "redshirt" is used to describe a student-athlete who does not participate in competition in a sport for an entire academic year. If you do not compete in a sport the entire academic year, you have not used a season of competition. For example, if you are a qualifier, and you attend a four-year college your freshman year, and you practice but do not compete against outside competition, you would still have the next four years to play four seasons of competition.
I have no idea where folks are getting the idea that a player like Luck has to apply to come back to Stanford next year...