On the flight from Phoenix to Las Vegas, I sat in the window seat aft of the wing. I got to see the flappy things move up and down. In fact, when they are totally up, you can see all the working stuff underneath them. And guess what, they are not called flappy things!
aileron – Either of two movable flaps on the wings of an airplane that can be used to control the plane’s rolling and banking movements. (dictionary.com)