All this ooblecky action takes place in The Kingdom of Didd. It's an idyllic, sleepy little kingdom (37), full of people who spend their lives catering to the King's every whim. If we zoom in a little deeper, we'll see plenty of other smaller settings, from the rooms of the workers to the castle turret. But all these settings fall under two big categories: inner and outer.
In the beginning of the story, Bartholomew is dealing with a problem inside the castle: namely, the King's giant stinkin' ego. But very quickly, the problem escalates and turns into an outside problem, raining down oobleck all over the kingdom. Despite his Chicken Little attempts to dissuade the King and the magicians, Bartholomew can't prevent the inner problem from quickly becoming an outer problem.
And as it turns out, the problem can't be fixed on the outside (i.e. there's no way to escape the oobleck). Because—if you remember all the way back to the previous paragraph—the root of the problem is on the inside. And sure enough, when Bartholomew helps cure what's inside (the King), that change spreads to the rest of the kingdom (outside). Voilà.