The way I see it, the main idea/goal with the Constant Speed Prop is that you are increasing the efficiency of the engine/prop combination at various power settings and RPM settings.

In fixed pitch aircraft, there are two basic types of props selected, the "cruise" prop and the "climb" prop.

The cruise prop has a higher pitch to it. In RC terms think of it like a 10X10 prop, it takes a large bite of the air. This increases top speed, but is slower to accelerate. This allows the aircraft to increase its speed at the most efficient power setting ie the cruise power setting.

The climb prop has a lower pitch to it. In RC terms think of it like a 10X4 prop, it takes a small bite of the air. This increases acceleration and climbing ability, but has a lower top speed. This allows the aircraft to climb faster at the highest power setting because the prop puts out a higher amount of thrust at lower airspeeds.

The constant speed prop, covers all of these bases. It is a "climb" prop at take off (Low Pitch/High RPM) and a "cruise" prop at cruise (High Pitch/High RPM). The constant speed prop also covers the gap between these two basic types of fixed pitch prop. Increasing the overall efficiency of the engine/prop combination.

I have an excellent graph somewhere that shows what I am talking about, I will try to upload it later.