Great question.
Turbo props and turbo fans, both produce thrust, but very differently.
In a turbofan, the turbine spends most of its effort turning the compressor blades. In a modern turbofan (TF) engine like GE 9x, you are looking at a 80-20 bypass ratio. This means, 80% of the air drawn from the front just flows through. Now, as the "FAN" (duh!) rotates, a huge volume of air is drawn in and compressed. As the volume moves deeper into the engine, the air pressure increases because the engine tapers down, as well as the compressor works in "compressing" the voume of air. As the air pressure increases, so does the speed and temperature. Now, as this compressed air exits from the back of the engine, it provides a forward thrust. The 20% air that DID get into the core, carrys on the combustion in the engine that provides the energy required to rotate the compressor blades. Now this is definitely simplified as there are many additional pieces, like stator vanes, equipment to shape and correct the velocity of the air, fuel injectors, igniters, afterburners (not in civilian airplanes of course) and many more contraptions.
While not completely comparable, a turbo prop (TP) behaves a lot like its piston counterpart. The turbine is simply replacing a traditional 4 stroke IC engine in this case and just tasked with rotating the blades. Each of the blade is a mini (well not so mini) wing that has the shape of an airfoil. As these rotate, they generate lift but since the rotational axis is parallel to the fuselage, it is actually thrust.
> Is it just cheaper to build a turboprop, and turbofans are the ultimate in terms of performance?
It is definitely cheaper to build a TP. And TPs can take a lot of abuse and needs miniscule maintanance compared to TFs. But if you are talking of raw performance, turbojets (TJ) actually run (fly?) around in circles around TFs. TJs are just incredibly wasteful, inefficient and needs a lot of maintenance.