The term "free power turbine" means an extra trubine that is not connected in any way to the main gas generating part of the engine. In effect we have a complete gas turbine engine with an extra turbine immediately behind it.
The purpose of the free power turbine is to extract power from the hot gas flow in order to drive the output shaft. This shaft is then connected to the propeller, helicopter main gearbox, or whatever else it is being used to drive.
The main advantage of this system is that the RPM of the free turbine (and hence output shaft) is independent of that of the gas generator. So we can have a constant speed propeller or helicopter rotor system, while allowing the engine to accelerate or decelerate as required to match the power required at any given stage of flight. This makes the system much more flexible in terms of the range of power output values available.
To understand what this means just consider how early turboprops worked. The turbines, compressor and propeller shaft were all connected directly together. To have a constant speed propeller meant having a constant speed engine. So opening the throttle to increase power simply increased the pressure and temperature in the engine, but left RPM constant. There is clearly a limit to how high such pressures could become before the egine started to surge. In reality the propeller RPM was usually allowed to vary within a specified range, then held constant only at very high power settings.
Other benefits include the ability to start engines with the propeller or helicopter rotors stopped (using a prop brake or rotor brake). So in a free power turbine engine the starter motor is required to spin up only the gas generator. This is obviously easier than spinning up the entire propeller or rotor system. So free power turbine engines are easier to start and are able to use lighter starter systems.
The principle disadvantge is that the system is a bit more complicated and slightly heavier, than it would be if the output shaft were connected directly to the gas generator.