What makes a souffle rise?
Short answer:  Steam.  

Long answer:  Proteins in egg whites are almost uniquely suited to making foams of tiny bubbles, then stretching like a web of bungee cords as the water inside these bubbles turns to steam in the oven.  Therefore, the critical element in making your souffle rise is the skill with which you whip the whites into a foam to the correct degree (just to stiff peaks, not over-whipped), followed by integrating (folding) that foam into the dense, flavor-filled base.  There are a few tricks for augmenting the rise -- e.g., using a pinch of tartaric acid in the whites, using a copper bowl -- but if your technique is poor, these things won't make enough of a difference.

Alton Brown ("Good Eats" TV show) has an excellent program explaining the whole thing, including some basic chemistry, available free on YouTube:
Part 1 
Part 2 

By the way, you said that a successful souffle must rise above the vessel.  While rising high is a major goal, I would not limit success to that event.  Last night, I made chocolate souffle that only crested the vessel a little ways (not the ideal "double the volume"), but each bite was still ethereal and decadent at the same time.  Everyone's plate was clean.  THAT, to me, is a successful souffle.