In a sandbox game, you are a player inside a virtual world (a sandbox with very distant
edges, like a playpen filled with sand). Instead of being offered levels in a pre-set order,
you roam around the virtual world and make your own choices about what goals you
want to achieve and how to set about them. Because you are making your own choices
right from the start, sandbox games have limitless possibilities. You make up your own
stories and move through the 3D world, learning new skills and features by discovering
them by chance and experimentation.

In Minecraft your player, or avatar, is called Steve. You direct Steve through the sandbox
virtual world to achieve whatever mission you decide. If you are successful in surviving
your first night against the monsters, you can follow your own enthralling
missions to interact with other participants of the game and build huge structures
limited only by your imagination.
A sandbox game allows you, the player, to make your own decisions about playing the
game, rather than being forced down a specific route by the game designers. You can
read more about this type of game design here: http://en.wikipedia.org/wiki/Open_
world. There is a little bit of mystery about why the player is called Steve, but you can
read more about it here: http://minecraft.gamepedia.com/The_Player.