The Safe is an item you can purchase from the Merchant after you have defeated Skeletron. It works as a separate private storage, just like the Piggy Bank and is separate additional storage from the Piggy Bank. It is able to hold items, just like any ordinary chest, except the safe's contents can only be accessed by the user who deposited the items. Buying another safe will not let you put more items in, but will allow you to transport items over long distances. This can be extremely useful when moving items from a single player world to another, or to a multiplayer world. Also, unlike the Piggy Bank, it can be placed on any surface.
Defeating Skeletron is required for the Merchant to have the Safe in stock.
Like Piggy Banks, Safes cannot be looted by other Players on a multiplayer map.
Safes can be used to expand your inventory by 39 units, meaning that you can put the important things in there, while you can carry the rest of the stuff.