In flight we want the rotors to turn at an approximately constant RPM.
But we want the power output of the engine to increase when we pull the collective up and to decrease when we push the collective down.
Power output of an engine is proportional to RPM. So we want the engine RPM to be vary with changes in collective position.
With a fixed turbine we cannot easily vary engine RPM without varying rotor RPM.
A free power turbine is connected to the rotor but not to the engine spools (the gas generator). So we can have a governor keeping rotor RPM consant by varying fuel flow to the gas generator.
If we up pole the rotors tend to slow down. The governor senses this and increases fuel flow to the gas generator. Gas generator RPM then increases to increase power output to restore the rotor RPM.
There are of course other advantages but that is the main one.