Over on New Scientist, they have a short piece on the mechanism of the Venus Fly-Trap. The leaves that make up the trap change shape from convex to concave, and this change in shape produces the rapid snapping action that is able to catch flies.
This sort of action is called snap-through in other contexts. You probably know it best from the popping of tops in many canned goods, where if it doesn’t give a pop on opening, you know the can has been opened before. These changes in shape from one stable state to another happen rapidly, which is the basis of action of the common dog clicker, which in a click operation undergoes two of these deformations.
This still leaves the topic of how this mechanism evolved. I’ll have to check with Nick Matzke on this, for he’s looked at these carnivorous plants in some detail.