Each slot represents a game you can play and save. If there is not a saved game available for the slot, it will be listed as a "New Game", otherwise there will be a brief description of the game and its progress.
To start a new game, find an empty slot and under it press it.
Games you have played previously or have completed will still hold up the slot space until removed. To remove a game from a slot, press the Clear This Slot button for that slot.