In college football it refers to a player who is not playing on a scholarship. In the NFL it refers to a player signed from open try outs in which the player signed was not scouted in some way.
When NFL football teams hold try outs that are open to the public a player who is signed that was not scouted in some way is known as a walk on. However, it must be noted that open try outs for walk on players are rare in the NFL. The Washington Redskins did try open try outs in the 1970s. The Philadelphia Eagles also tried open try outs in 1976 and ended up signing 30 year old school teacher and bartender Vince Papale. For the most part players who are not drafted are still scouted in some way and invited to a work out in which the skills of the recruit are tested.