ORIGINAL: Charlie P.
Aeroelastic flutter. Same principal that causes a flag to flutter in the wind. Caused when the center of lift is ahead of the center of gravity of the control surface.
You can fix it (or reduce it) several ways.
Slow down.
Add a counter-weight to bring the C.G forward.
Tape the hinge line to seal out turbulance (sometimes helps).
Use beefier hinges, horns and connectors.
Make the aileron thicker than the trailing edge of the wing it attaches to.
Note that there are some planes - 3D models especially - that have so much control surface in relation to the wing that they might tear off if you fly too fast.
To Charlie's ( excellent ) post I'll add...
You can also add bracing or supports, ala "flying wires".
Check out some in flight YouTube videos taken with on-board cameras on RC planes, particularly those that look over the wing or elevators.
It is scary how much flex there is on most RC model wings and particularly elevators.
It is quite simple to affix a carbon rod to each elevator half that angles off onto the fuselage, much like a guy wire. This adds a LOT of stiffness to the tail and rudder.