The ECM can tell when the EGR is functioning properly by watching for changes in NOx via the O2 sensors. When you reintroduce exhaust gasses into the combustion process, in the correct amount, the level of NOx in the exhaust system drops significantly. Too much of the exhaust gasses introduced in to the intake charge and you do not get complete fuel burn causing the fuel level in the emissions to rise drastically. Too little and the NOx levels stay high.
Pretty simple actually.