Or to amplify the signal in an FM transmitter(a real one) up to the tens of kilowatt level,so that the signal will be nice & loud for the FM receiver in your car.
You use a power amplifier if you need to micro-step a stepper motor in a robotics application, or drive a coil in NMR ( nuclear magnetic resonance), MRI (magnetic resonance imaging) or EIT (electrical impedance tomography).
It is required to drive the spindle motor and linear head seek motors in disc drives.