In layman terms Sandbox Game is a game play and structure where the user has the free will to make decisions regarding the story of the game. There is no set of story mode or structure of the game or predefined notion which the gamer has to follow. Sandbox games are also called free world or open world games as well. Some might differentiate between sandbox games and open world games with respect to the brand that the game is being launched from. Some consider GTA and FarCry as open world with their attentive gameplay and user chosen storyline as being exciting and enjoyable. In comparison to the games Just Cause 2 and Crackdown as being sandbox games because their gameplay is not enjoyable and user’s feel it as useless to play.
In marketing terms many game releases are marketed as both Sandbox and Open World games just to give them an edge and understandable for the people who might know the type of game by one name. In a technical way you can say that Sandbox Games are non linear in nature where the gamer is responsible for setting up the storyline, missions and gameplay. Good examples of Sandbox Games are GTA 3 onwards and Minecraft.
Sandbox games do have limitations or areas which are closed to the gamers. There are many reasons for that such as the player has to complete a certain mission to open that area or the area is shut down due to map constraints, size constraints, engine constraints or creative decision making limitations.