Flutter is an unstable oscillation which can lead to destruction. Flutter can occur on fixed surfaces, such as the wing or the stabilizer, as well as on control surfaces such as the aileron or the elevator for instance.
On the following video, you will see how flutter is affecting the stabilizer of a small airplane. You will also see a comparison of flutter with the collapse of the Tacoma Narrows Bridge in 1940 :
The start of a resonance vibration in torsional mode resulted in the collapse of the bridge. This is an example of forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency of the bridge to eventually destroy the structure. This vibration was caused by aeroelastic fluttering.
Comparison with a swing :
When a father pushes his kid on a swing, the motion of the swing has a natural frequency. If the swing comes back every 8 seconds, its natural frequency is 1/8 = 0,125 Hertz. Now if the father wants to maintain the motion of the swing, he has to push it each time the swing comes back to him, which means every 8 seconds. The force used by the father to push the swing every 8 seconds is the external force applied with a periodic frequency. If the father does not push the swing at the right moment (i.e. every 8 seconds), he will damp the motion and the swing will not go as high as the kid would wish. However if the external periodic frequency of the father matches the natural frequency of the swing, we get a resonance vibration. The resonance vibration will allow the kid to climb back and forth as high as he wishes with his swing.
On an airplane, the wing attached to the fuselage has a natural structural frequency. The relative wind and the aerodynamic force that it generates on the wing represents the external force which is applied with a periodic frequency. When the periodic frequency of the aerodynamic force is the same as the natural structural frequency of the wing, the system enters resonance vibration and the amplitude of the vibration becomes important. If it goes on for a certain time, the wing will break.
you will find more details about the destruction of Tacoma Narrows Bridge, resonance vibration and aeroelastic flutter in the following footage :
The next video shows how an airplane flies by flapping its wings as a bird because of flutter :
How to avoid flutter ?
The constructor should design the airplane in such a way that it will not suffer from flutter below VNE (Never Exceed Velocity) or below VMO/MMO (Max Operating Velocity or Mach number). So, do not fly at a speed greater than the red line (for SEP, Single Engine Piston, and MEP, Multi Engine Piston) or at a speed greater than barber's pole (VMO needle on jet airplanes).
Technically, how flutter develops ?
The wing is a very flexible part of the airplane. While standing on the ground, you can move the wing tip up and down very easily with your hands. So imagine now the aircraft flying during the cruise while the total lift equals the weight of the airplane : each wing is supporting half the weight of the airplane. Both wings are bent upwards. Now let us say that because of a gust the aircraft is shaken up and down, then the wings are flapping up and down because of inertia. If the airplane is not subject to flutter, then the vertical vibration of the wings is damped and it does not amplify. However if the periodic vibration of the gust has a frequency similar to the natural structural frequency of the wing, it will enter resonance and the up and down deflection of the wing will be increased, amplified, and eventually lead to its destruction.
In fact, when the wing tip is going down, a vertical relative airflow is hitting the lower surface of the wing, increasing its angle of attack, increasing the upwards aerodynamic reaction (Lift) on the wing tip. When the wing tip has reached its lowest point, the extra Lift generated combined with the elasticity of the material is acellerating the tip upwards just as a spring would do. Now, while the wing tip is moving upwards, there is a downwards relative airflow on the tip which is decreasing the angle of attack of the tip, thus decreasing the magnitude of the Lift. When the tip reaches its highest point, the Lift is low or even directed downwards. That negative lift is helped by the elasticity of the wing and again, as a spring would do, the system is now accelerated downards again. If the frequency of the gust matches the natural structural frequency of the wing, a vibration in resonance is developing, aeroelastic flutter takes place and the aircraft will be flying by flappings his wings as a bird would do. The only difference with a bird is that the bird will not break his wings because of flapping it.
In the following footage, you will see the aeroelastic flutter of the horizontal stabilizer of a model airplane (Bronco aircraft, with a double vertical stabilizer) :