How Zelda:TP exploit works - stack buffer overflow

During a stack buffer overflow, program writes outside of the intended program data structure in the memory address.

This is used in the Twilight Hack, when you are in game, a lengthy name of Epona - the horse is used to generate a stack overflow. This occurs during the conversation with the man near you when you load your save, when he loads the name to use in the dialog box or when you are entering the next zone, where you have to ride a horse.