If I remember correctly, EGR reduces emission of nitrous oxides (NOx). By adding a little exhaust gas to the air/fuel mixture, the flame speed is reduced. On ignition, the flame front advances from the spark outwards. Diluting the mixture slows the flame front down, which in turn reduces peak temperatures. As NOx are formed at very high temperatures only, reducing the flame temperature reduces the formation of NOx, making our cars a little more furry animal-friendly. Apparently, it doesn't affect performance (much).