My math professor in the past explained it this way:
Consider yourself a 2D creature(some sort of pancake). If placed in a circle, you can't escape in a 2D world.
But in a 3D world this is simple. You could just jump up and disappear and reappear before all your 2D friends outside of the circle.
Now consider yourself a 3D creature(some sort of meatball). If placed in a sphere(football?), you can't escape in a 3D world.
In 4D, just "jump" and reappear on the outside!
Anyone any thoughts about this?
Or a better explanation?