You could think of it as being made up of two parts:
The first part is the Gas Generator, which is a self-contained jet engine complete with compressor, combustion chambers and turbines. The turbines extract enough energy from the exhaust gas to drive the compressor to keep the Gas Generator running.
But the exhaust gas flowing out of the gas generator still contains a large amount of energy. The exhaust gas
The purpose of the Free Power turibine is to extract energy the exhaust gas to drive the propeller.
The Free Power turbine is not directly connected to any of the rotating parts of the Gas Generator. This means that the RPM of the Gas Generator is not directly related to that of the Free Power Turbine. So we can have a constant speed prop, driven by a constant speed Free Power Turbine.
When we want more power we increase the fuel supply to the Gas Generator. This causes the Gas Generator RPM to increase, thereby producing more high energy exhaust gas. This tends to make the RPM of the Free Power Turbine and the prop to increase, but the prop CSU will increase blade pitch to prevent this.
In older coupled turbine turbo-prop engines the compressor, turbines and prop were all connected together. This meant that to have a constant speed prop we had to have a constant speed engine. So when we opened the throttle the extra fuel increased the pressure and temperature in the engine, but the CSU prevented the RPM from increasing. This made ir more difficult to get the engine to operate over wide power range without surging.