Some discussion here:
http://rpg.stackexchange.com/questions/ ... ndbox-play
When I use it, I tend to mean an open environment in which the characters may go anywhere to find their own adventure. For convenience, this can be keyed hexes with short descriptions the CK must fill in on the fly, supplemented with random tables for encounters and flavor by location, terrain, etc. There may be some setting, background events, factions, etc. but the players bumbling through the environment is the cause for most conflict and interest in the game.
When I run a sandbox, it usually has some home-made set pieces or tie-ins to get to published adventures, so that the players can have some structure when they want it. Also, the world becomes more rigid with use: a place stops being random once it's been explored (or by the next session they revisit it) and I'll fill in the blanks with encounters between games, focusing on places they are likely to go next.
Contrast with a game in which you show up at the dungeon door, and if you walk away, the module is over, and you may as well go home (which is how some Basic D&D games possibly went until the Expert Set gave you rules for getting to and from).
Some published adventures are 'sandboxy' in that you have a lot of people and places to visit in no particular order, and there are many possible outcomes; the players skipping parts or redefining their goals doesn't wreck the game.
Note that if you handle the players going to the wrong place by just making the place you wanted them to go THAT place, it's not the same thing; in that case the players really didn't have any self determination, though it's partially philosophical as they didn't know that.
I think it's pointless to strive for any kind of purity in sandbox gaming. I think a lot of games are sandboxy to a degree. I think games that are are usually better for it, though sometimes a modules that is clear; go here, then here, then here or here, then fight the boss, while a little railroady also has the benefit of being self-contained, stays on track, and finishes in a reasonable amount of time so something new can be played.
The Wilderlands setting is a good example of a published sandbox. It has a lot of mechanisms for providing adventure no matter how "off route" the characters go. Fixed adventures that take place in the Wilderlands also are available, which are little pockets of more structured adventure. Though if a character leaves the adventure area for that module, the world probably doesn't fall apart, though the Judge may be angry that he or she had to spend money on the adventure.
I think probably most sandboxes are home grown. You make a city, describe a few areas around it, maybe place a few dungeons, and then ask the players where they go next. If they go into an unplanned area, do the best you can with whatever tools you have: random encounter, make something up, whatever. Then write down what happened and mark it on the map. Before next session figure out how mobile they are and plot a few more areas. If they go to them, cool, if not repeat what you did last time.
Sandboxes are often "hex crawls" because many published examples of sandboxes are hex crawls. But they don't have to be.
Sandbox games are really good for players who have background and concepts they want to explore because those things become the game, instead of just descriptive moments between completely unrelated adventures.
