A sandbox game is one in which there is a whole simulated world, or at least a large region, and you can go anywhere and do anything you want. There is no imposed quest or specific goal, and no linear series of things that you have to achieve in order. Sandbox games are also called "open world", and the concept can apply both to traditional tabletop roleplaying games, and many video games.

Many traditional games involve the GM setting up a specific dungeon or adventure for the players, and then using plot hooks or simple fiat to get the players tackling that adventure. A sandbox style game is very different. The GM will give the players a map of a large region, maybe a kingdom or continent, and simply say, "Where do you want to go?" They might explore, or they might seek rumours and stories of adventurous locations, and then decide where to go and which ones to check out. They may stumble across monster lairs or old abandoned dungeons, in any order depending on which direction they decide to travel.

Such a game can require more work from the GM, who needs to adapt to the whims of the players, but can be very satisfying for everyone.

Transcript

GM: This might be a good place to stop for the night.
Rey: But I still haven’t learnt about my mother! I haven’t achieved anything this session!
Chewbacca: Do you remember the first session of your fantasy campaign?
Luke: We just sat around all night trying to figure out supplies and inventories.
Rey: It was a wide open sandbox! You could have done anything.
Chewbacca: Ventured out into the wilderness and got eaten by the first monster we came across?
Rey: Exactly!
Chewbacca: So is it any wonder we wanted to take careful stock of our situation first?
Rey: Getting eaten would have been more exciting!
Luke: He does have a point there.