I hope this is in the right category! Good education helps good aid in repairs right?
After reading the wikipedia article on EGR systems I was dissatisfied with the explanation and thought I could write a better one to replace it. I hope for it to be factually correct and simple to understand.
Please edit or rewrite my explanation if you think it can be better.
For every cycle of the combustion chamber within a internal combustion engine, a charge of air is drawn in during the induction phase. Without an EGR valve almost all of the oxygen in the air is burned when it is mixed with fuel and ignited. This creates heat, raising the temperature of the combustion chamber. When at peak temperatures the nitrogen and oxygen present in the air of the next induction phaze react causing NOx. An EGR valve aims to reduce the peak temperatures of the combustion chamber by replacing a percentage of the intake air with non combustible (inert) exhaust gasses. Less oxygen, less combustion, less heat, less NOx