EGR is considered a `metered intake leak' and was developed to reduce the combustion temperatures to below 2,500 degrees, the threshold where NOx is created. Not unlike putting a brick in your lavatory to lower the volume of water used, the EGR valve meters a readily available inert gas (actually exhaust gas which contains a lot of very inert Carbon Dioxide) into the combustion chamber to effectively reduce the volume. Smaller effective displacement means less fire, and less heat and thus lower temperatures, thereby controlling NOx emissions.

In a typical automotive SI engine, 5 to 15 percent of the exhaust gas is routed back to the intake as EGR (thus comprising 5 to 15 percent of the mixture entering the cylinders). The maximum quantity is limited by the requirement of the mixture to sustain a contiguous flame front during the combustion event; excessive EGR in an SI engine can cause misfires and partial burns. Although EGR does measurably slow combustion, this can largely be compensated for by advancing spark timing. Contrary to popular belief, a properly operating EGR actually increases the efficiency of gasoline engines via several mechanisms:

Reduced throttling losses. The addition of inert exhaust gas into the intake system means that for a given power output, the throttle plate must be opened further, resulting in increased inlet manifold pressure and reduced throttling losses.
Reduced heat rejection. Lowered peak combustion temperatures not only reduces NOx formation, it also reduces the loss of thermal energy to combustion chamber surfaces, leaving more available for conversion to mechanical work during the expansion stroke.
Reduced chemical dissociation. The lower peak temperatures result in more of the released energy remaining as sensible energy near TDC, rather than being bound up (early in the expansion stroke) in the dissociation of combustion products. This effect is relatively minor compared to the first two.