RPM, basically, is related to power and to prop pitch. By reducing RPM you're lowering the revolutions per second (duh) which uses less fuel.
When you decrease RPMs past a certain point, your MAP (that your throttle controls) drops with it, further conserving fuel.
Also, as you reduce RPM, the prop pitch changes, reducing the amount of work the engine has to do.
You can watch this as you come in for a landing. Set auto angle (ctrl X) and pull up E6B. Turn engine off, and note speed. Now reduce RPM and watch your speed jump! Now increase RPMs to max again and watch your speed slow down (while in a descent)!
I think less RPMs = greater prop pitch, making the prop closer to being feathered than at full RPMs, which = narrower bite into the air for the prop, but creates an airbrake for the plane.