The picture below is a simple guide to how the EGR (Exhaust Gas Recirculation) works. Fuel and air get mixed up via the intake and combusts in the cylinders (note the weird spelling in the picture below!). The unburned gas is then sent down the exhaust and out in to the atmosphere via your tailpipe. For this simple explanation we can ignore how the turbo works in our engines.
However, EU regulations state that manufacturers need to reduce their NOx (Nitrogen Oxide) emissions in order to help save the environment. The easiest way they can do this is to take some of the exhaust gas and pump it back through the engine to be burnt again. This secondary burn process reduces some of the NOx emissions so they can meet their targets. They want us to ignore the fact that most of their senior CEOs fly around in private jets putting out way more NOx emissions than us simple car/truck/vandrivers ever will!