Sandbox or Playground

A World of Opportunity Awaits!
It has become common to use the term "sandbox" to describe a certain old school style of campaign play in which the referee creates a setting and sets the players free in this setting to explore and follow their interests according to their own timing. It's an open world concept where there are things to interact with and adventures to be had, but there is no set plot or preconceived story. It may involve the referee furnishing the players a map, perhaps with hexes printed on it. Moving from hex to hex and rolling for encounters is termed a hex-crawl which can be a type of sandbox. The open world empowers the players to shape the game.
For some players presenting the "empty sandbox" where anything is possible can result in paralysis. The referee who places a map before the players which shows a village, a forest, a road, a stream and a castle and asks "What do you want to do?" may be asking a very difficult question.
Perhaps redefining the setting as a playground would be more appropriate. A playground typically offers a number of objects, clearly visible, which can be explored and interacted with in a manner that encourages use of one's imagination. Children develop elaborate narratives to go along with their playground adventures and I see no reason why our adult role-playing cannot offer a similarly rich and rewarding experience. By placing a number of easily recognized opportunities into our setting, things such as rumors, reward offers, a treasure map, help wanted, abandoned mines, ruins, and old legends, the referee can make things easier for players to decide what they want to do. Populate your setting with possibilities and inform your players that it is up to them to decide what they would like their characters to investigate further. If the players decide to ignore all of your "hooks" and go off on their own, perhaps for a walk in the countryside (or want to take over the local tavern) that is all the better. By providing a rich and varied environment you have set the stage for your players to explore and have adventures.