For an airplane, the airframe is the body, the engine is the heart and the avionics are the brain.
The airplane of my affections has two hearts, a pair of Pratt & Whitney PT6-A20 (or PT6-A27 for later models) engines. These are is reverse-flow free turbine engines with a three-stage axial compressor, a one-stage centrifugal compressor and one power turbine. Let me elaborate.
Engines work by taking advantage of the fact that when you burn fuel in air, the products of the combustion take up a lot more space than the reagants, both because there are more molecules, and because the heat of the reaction makes the gases expand. The more fuel you burn, the more power the engine produces, but in order to burn more fuel you need more air, so part of engine design is devising ways to cram more air inside. Going fast through the air helps, but it's useful if the engine to work while the airplane is standing still, too, so we compress the air before burning it.
The picture shows a larger version of the PT6, with two power turbines. The propeller is mounted on the front of the engine, the left side of the picture.
An axial compressor stage consists of a spinning disc called a rotor, and an adjacent non-spinning disc called a stator, each fitted with very carefully engineered airfoil blades. Intake air is accelerated and compressed by the spinning rotor and then further compressed as it slams the stator, sort of like your car would be if you drove off a freeway ramp into a concrete wall. The stator also helps to prevent the airflow from spiralling around, keeping it parallel to the axis of rotation of the rotor, hence the name axial. As one rotor plus one stator equates to one compressor stage, a three-stage axial compressor is like a row of half a dozen doughnuts, with every second doughnut spinning around. In this case the first spinning doughnut is titanium and the subsequent two are stainless steel with cadmium frosting. The blades on multistage compressors get smaller and closer together as the pressure increases down the line.
Air exiting the third stage of the axial compressor enters a centrifugal compressor, an additional doughnut in the row. As it spins, it flings the air outward, into a chamber called a diffuser, which slows it down, thereby compressing it further. At take-off power, this air has a temperature of 280 degrees celsius and a pressure of 103 psi.
This compressed air enters the combustion chamber where fourteen nozzles add fuel to the continuously burning mixture. The temperature in the combustion chamber is so high that the walls of the combustor can't actually withstand it. The airflow is made to provide a cooling layer that keeps the fire away from the walls. So turbine fuel is burning at 1050 degrees celsius, less than six feet from my head, and what's keeping it in there is air. Whee.
Instead of burning through the combustor, nacelle, or my head, the hot expanding gases are directed to the compressor turbine, which they spin at a rate that can exceed 37,500 rpm. That's called NG, N for number of revolutions per minute and G for gas generator, another term for compressor. The compressor turbine is on the same shaft as the compressors discussed above, and is what provides the power for their rotation. About two thirds of the power generated by the engine goes right back into turning those compressors. The accessories gearbox, also on that shaft, runs useful things like the oil pressure pump.
After the compressor turbine, the gases pass through the power turbine which spins its own shaft at up to about 33,000 rpm, called NF, supposedly F for fuel. (F for fuel and G for gas: about as useful as GUMPS, eh?) The shaft drives the propeller through a 15:1 reduction gearbox, for a maximum propeller speed (Np) of 2200 rpm.
The limiting component for engine temperature is the vane that guides the expanding gases to the compressor turbine blades, but it's so hot there that the temperature (T4) cannot be reliably measured. The temperature is measured instead between the compressor turbine and the power turbine (T5), and the pilot memorizes a little table of values for T5 that correspond to the maximum allowable temperature for T4 at various phases of flight.
Free turbine refers not to the price of these things, but to the fact that the power shaft has no physical connection to the compressor shaft. The ends of the two are aligned, but there is about five millimetres of space between them, and they rotate in opposite directions.
Reverse flow means that air goes in near the the back of the engine and exhaust comes out near the front, the opposite of your regular jet engine. The exhaust is still directed backwards, though and its discharge adds an extra twenty-nine horsepower of thrust to the engine output.