The wave accelerates the electrons in a metal due to their electric field, i.e. electric currents are induced. The electrons in a metal are not bound to any specific ions but can move freely. However the accelerated electrons can also scatter from the atomic cores and thus loose the energy they received from the electric field creating thermal motion of the atoms, i.e. heat. That's the reason for the resistance of metals.
In a radio, basically the currents induced are used to move the membrane of the loud speakers. This also diminishes the current as the energy of the currents is converted into sound waves.