my understanding..
-running rich means your running a higher fuel to air ratio which results in a much higher degree of ignition in the cylinder chamber when the fuel is ignited. This leads to a better stroke of the piston leading to more power being generated. This type of setup is usually seen in highly modified and high performance cars. All the internals of the engined are modified. Examples include engines being bored out, larger and heavy duty cylinder heads, platinum spark plugs, aftermarket distributor, pure copper wiring..etc. Bad side is that you spend a hell of alot of fuel, your average is horrible and you wear your engine out alot quicker then normal setups. But then again you do enjoy that extra power.
-on the other end running lean means that your running less fuel and more air. Leading to a more economical fuel consumption and better averages. But the down side is that engine itself is underpowered and you don't get the power that we all crave for.
hope this helps. if i m wrong please do correct me.
