The Debug mode is there for testing reasons most of the time. It's intentionally programmed in so the developers can test a variety of scenarios and easily set up certain situations (like having a particular set of equipment and/or materia) without having to play 20 hours.

Devices like GameShark and Action Replay that mess with the game's code can access the Debug Room when it wasn't meant to be. It's confusing and weird because it wasn't designed to be user friendly, meaning the gamer is never supposed to see it. I've never owned a GameShark or anything, and I've never seen the Debug Room for myself, so I couldn't tell you more than that.