The term "rail" has three meanings in the horse world.
1. In racing, the rail is the fence that marks the inside edge of the race track.
2. In showing, and sometimes general riding, the rail is the outer fence or wall of the arena. An instructor may, for example, insist a student keep their horse "on the rail" which means riding around the outside edge of the arena.
3. In jumping, a "rail" is horizontal element of a jump.
Riding "on the rail."