A sandbox game is a player-driven game. Rather than deal with a metaplot or outside forces, PCs wander about in search of excitement. It is so-called because there is no natural endpoint or winning condition in the campaign, and play is largely unconstrained rather than programmatic.
The opposite of a linear game.
Sandox games as a genre
Calling something a sandbox game implies a number of characteristics:
- The primary meta-game goal is discovery/exploration, which subordinates the meta-game goals of plot and cohesion
- The game is high on GM control of background, but low on GM control of events. In terms of trajectories, they remain constant until affected by the PCs, and the secondary effects of the PCs' actions.
- The environment is rich in things to do, rather than one thing being obviously more interesting than other choices.
- Encounters and events are emergent rather than programmatic.
- When the players affect the environment, the GM presents logical consequences from a realistical standpoint, rather than a poetic viewpoint.
Tweaking any one of those items would change the game. For instance, if the players defined the world collaboratively and asked the GM to "tell them a story" with them as the characters, you would have what White wolf calls a storytelling style but which might be more specifically called an existentialist-storytelling style. In poetic terms, it resembles the storytelling style of someone telling a bedtime story... meaning is intended, but the audience presents the situation and no particular end to the story is mandated.
Conversely, if it has most of the sandbox elements, but there is really only one interesting thing to do, it looks like the classic delve/quest style.