Why is energy conversion important?
Because it is very often naturally occourring or requested in human activities.
For example, in the Sun, nuclear energy is converted in electromagnetic energy in natural manner because the system must go to a future equilibrium.
Or for human activities... in a loudspeaker, the electromagnetic energy is converted in mechanic energy and in acoustic wave because we want to hear recorded music or voices.
To close, also a falling ball is a very simple example of energy conversion (potential to kinetic).