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In a typical MVC app, the 'enter' method of each state would set up the appropriate models, views and controllers, and the 'exit' method would do the corresponding teardown / cleanup. You could tie this to the history API (or history.js) to support URL linking and navigation.
But states can mean anything you want as long as only one of them can be active at any time in a given context (StateManager). In a Vim implementation you could manage the normal / insert / visual editing modes using States. In a space shooter game, you could have the player spaceship be in normal, shielded, dead, etc states.
The link to Backbone is extremely thin and basically limited to using Backbone's event system to trigger state change events.
