What is aeroelastic deformation?
Aeroelasticity is the elastic deformation of a structure caused by aerodynamic forces. An example is the flexing of a wing. The change of the shape of the structure has in turn an effect on the aerodynamics. 

Aeroelastic effects can be static, such as the upward deflection of a wing under the influence of lift, or dynamic. 

In the static case, the aerodynamic for cause the structure to deform. If the structure is very flexible this can cause a stability problem: the deformation causes an increases of the aerodynamic load, that will in turn increases the deformation until the structure fail. 

In dynamic cases there is an interaction between the aerodynamic forces, the inertial forces and the deformation of the structure. Usually the dynamic behaviour is transient and damped. 

When the dynamic behaviour is undamped (the aerodynamic forces add more energy than is dissipated in the transforming structure) an increasing vibration will occur. This is called flutter. Flutter is unwanted the because the resulting severe vibrations can cause structural damage. 

Here is an example of flutter on a small aeroplane: