The NOx problems were mostly resolved through the injection of urea into exhaust gases (e.g. AdBlue), dramatically reducing NOx emissions while leaving the efficiency and power unaffected. Urea systems add an extra cost and complexity to the vehicle though (not to mention that you need to top up your urea additive occasionally), and VW seemed to find a loophole that allowed them to make small, inexpensive cars without urea injection. They did this by injecting fuel into the exhaust in the absence of Urea, but to achieve the same effect. But this can gunk up the NOx trap if used endlessly (it is far less precise than urea, obviously), reduces fuel economy, etc, so they built this One Little Trick that only actually does that during identified tests.