Think of the stages as items, or parts, placed one after the other. Think of the axial stages as fans. Picture one of those big square ugly floor fans that used to get put on the floor in your gradeschool classroom. Put one in front of the other, the first blowing into the second. This is a two stage axial compressor (albeit a very inefficient and cheap one).
Add a third fan, and you have a three stage axial compressor.
After the axial section, you have the centrifugal section. Typically only one centrifugal compressor is used. If there is only one centrifugal impeller, then it's a single stage centrifugal compressor.
Therefore, you have a two stage axial, single stage centrifugal compressor. It sounds confusing, but really all it's doing is describing each section in turn, to describe the whole compressor.
An important function of these compressor types is that they typically are independent of each other, in the way they're driven. The compressor wheels, or stages (same thing) are driven by the turbines. Remember that the turbines are driven by hot, high velocity, expanded gasses coming from the combustors.
The PT6A gets a little confusing because airflow reverses several times inside the engine. It does this for two reasons; one is to preclude passage of contaminates and materials which might damage the engine (including water or ice, which may not only cause damage, but put out the continuous flame in the burner can...a "flame out"). The other reason is to make the engine as compact as possible, and to increase the strength of high stress parts by making them short and stout.
It would be easier to see the layout of the engine if it went in a straight line; you could conceptualize it better, but in the case of the PT6A, it doesn't do that.
As hot gasses exit the combustor, they pass over the power turbine wheels. The first turbine wheel drives the high pressure compressor. This is typically the centrifugal compressor(s). It does this with a shaft that runs directly from the first stage power turbine, right down through the middle of the compressor, to the high pressure compressor. This shaft is hollow.
After the hot gasses pass over the first stage power turbine(s), they pass over other turbines. These turbine wheels are attached to a shaft that goes right up the middle of the hollow high pressure shaft. This smaller inner shaft connects to the axial compressor wheels, and drives them. This turbine is called the low pressure turbine wheel.
Therefore, the compressor wheel is driven by a specific part of the power turbine section. This is called a spool, and we have single, double or triple spool engines.
On turbofan engines, and on some turbopropeller engines, certain spools drive the fan, or propeller. On the PT6A, the main reason it's a reverse flow engine is that the exhaust gasses drive the propeller. There is nothing connecting the compressor and turbines to the propeller. Hot gasses exit the engine, and drive the propeller; it's independent and free of the mechanical opeation of the power turbines and compressors.
To think of it this way, in abstract theory you could grab hold of the propeller on a PT6A and start the engine. The engine would start, and the propeller would be immobile as you held it. In truth, there's just too much torque on that prop; you're going to get tossed. But the point is that the only thing driving that propeller is hot air; there's no mechanical connection between the actual gas turbine engine, and the propeller itself, as far as driving it.
We call this kind of engine a free turbine engine, because the engine is separate and independent of the propeller. Other turbopropeller engines, such as the ubiquitous TFE-331, drive the propeller directly via a shaft and gearing. These are not free turbine engines, as if the engine is turning, the propeller is turning; they're connected.
Turbofan engines work the same way; the fan is driven by planetary gearing from the power turbine section, via a concentric shaft that runs right up the middle of the engine. It connects a spool (power turbine, and compressor) to the fan, through a planetary gearbox.
It's important to note that the different spools of the engine aren't connected. The only connection between them is that compressed air and hot gasses flow from one to another. In a single spool engine, everything is connected. But in a two spool or double spool engine, the high pressure and low pressure sections of the engine operate independently of one another. One influences the other, but the first stage power turbines/high pressure compressor(s) that make up the high pressure stage will be moving typically at a much higher speed than the other spool(s).
Hopefully this isn't confusing you more...
