Your bed is where you can save your game at any time before you enter a dungeon. It is also where you wake up every morning after having adventured in a dungeon. The mailbox is where you receive your mail. Mail can consist of either Pokénews or rescue requests. From your mailbox you can organize your missions, accept or decline rescue requests as well as read and store Pokénews. You have to take the old mail out of you will not receive anymore.