The term originated in computer games and there it typically describes a game where it's playing field is wide open for the player to do what they want. Around 2005 with the release of Necromancer Game's Wilderlands of High Fantasy Boxed Set, it's authors, I am one of them, used it to describe what made the Wilderlands different than other setting. The boxed set was designed to make it easy for the referee to adjudicate his players roaming freely across the map.
Later the term got attached to a specific playstyle where the players wander the landscape without direction from the referee. However this is beyond what myself and other Wilderland authora intended. The problem is that when people take the hard core simulation of wandering the map too literally. This often results in frustration as many PC groups feel rudderless and the game without direction. In fact if you read through various forums posts, like at Enworld, you see these campaigns fail more than they succeed.
The trick to overcome this is World in Motion. You work with the characters to give them a background they like in the setting. This provides a framework in which the players can make his initial choices. This background can incorporate what some consider railroad elements like being members of a noble household, a guild, a temple, etc. But the key difference is that the players are free to leave or ignore those elements as long as they are willing to suffer the consequences.
Along with this you develop a timeline revolving around NPCs and events. This timeline is created with the idea that this is what happens if the player didn't exist in the campaign. This timeline becomes your plan. It gets altered as a result of the consequences of the player's action. At some point the campaign will become self driving as the consequences of the consequences start propelling the players forward.
Again the Sandbox was meant to describe a type of setting not a playstyle. But you can't control how these things go on the internet so hence the confusion.