During the combustion process the flame front propages and consumes the burnable mixture, thus expanding the heated gases which push the pistion down to transmit mechanical energy.

When you're lean, you'll start to detonate (multiple flame fronts and basically an explosion rather than a combusion). If you're really lean then basically you'll just be heating up air because there's not enough fuel and that basically will get you no where. I guess this could be considered partially as a flame out.

A flame out is when you run too rich, thus fouling the plug and robbing it's ablility to stay hot. Therefore you will not have a source to initiate the flame front, hence 'flameout'. Too rich of a mixture will douse the fire.