Sandbox is a "Gamemode" of sorts for PW, it's original purpose being a means to play in a non-dedicated match and to test out an army, or an army's new units. Sandboxes usually have very relaxed rules and always are in a "declare" turn order, this means that basically the battles occur quickly to allow optimum testing of armies and to allow newer members to practice their effects and poses. They are usually quite popular among newer members but tend to have periods of inactivity due to the combatants moving onto more interesting/dedicated matches.
Similar to DTK, sandbox has developed several game modes within itself. Classic, Destruction, Evolution and Farm.
This is the most common of the sandboxes and features non-limited armies and incredibly lax rules. You tend to start your PW experience in a sandbox as they are the most helpful way to get into the action.
Destruction sandbox usually has a strict "peace time" of sorts where limited combat occurs. This is to allow all the players to build up a huge and detailed city. After a certain amount of turns, or when the OP deems so the "peace time" is shattered and players are able to wage war, from small scale infantry combat to huge scale titans ripping chunks from buildings.
Probably the least well known of all the Sandboxes, evolution is a much more calm and action-less form of sandbox and can sometimes lead to a whole new army. The general idea is to start of with an incredibly simple organism, from this new ones are born with different traits and through natural selection move on to create the next stage of that race's life. There is limited combat and it is usually more fun to play, then watch.
Another common sandbox mode is the farm, however this is used by a single person to show the mechanics of their army. It can also be used to tell stories of that army's past or provide a new story to add to that army's fluff. Unfortunately due to lack of competition the farms tend to die early on.