Some people thing about constant speed propellers like shifting gears in cars. The analogy sort of works.. in that as the plane goes faster (or slower) you can change the pitch of the propeller to keep it spinning at the same rate by "grabbing" more or less air. Fixed pitch props are kind of like having your car stuck in third gear.. people find a balance between climb and cruise performance, but usually all this means is that you end up with a plane that doesn't climb that great, and can't really cruise much over 110-120 TAS.
The turbo works by keeping the engine producing power levels similar to what you get at sea level (usually) even up at altitude where the air is thinner and you'll usually only make around 55% power even with WOT. Super chargers do the same thing, the difference being that turbo's use the expanding exhaust gases to spool them up and force air into the intake manifold while super chargers use a mechanical drive from the engine. Turbo's do add some back pressure on the exhaust, but I'm of the conjecture that it's more efficient than a super since you are utilizing expanding exhaust gases that would otherwise have gone to waste
So, putting the two together (turbo / constant speed prop) you have an engine that can continue to make full power up at altitude, and the adjustable pitch prop keeps the propeller in an optimum power band, so you can "shift gears" as you go faster and keep the prop somewhere around 2,200 to 2,400 RPM
Also.. air does get thinner as you go up, but it tends to loosely "balance out" in favor of the airplane. IE, sure the propeller has less air to grab onto, but the plane also has less air to fly through.. that's why given a constant engine man press and RPM you'll pick up a few knots of TAS the higher up you
*PS.. faster spinning prop is not always better.. in fact, turboprop planes spin relatively slow. So there's an optimum speed that works for the aircraft props too. One criticism of Cirrus no-blue-knob is that the 2,500 RPM they're set at is a little too fast. I trust the engineers know what they did, but there are people out there who believe 2,200 - 2,400 is a better cruise regime