How does the Bugatti Veyron 16.4's motor work?

It works in the same way that all 4 stroke, internal combustion, petrol engine, works.

The veyron has it's cylinders arranged in two main banks like a V8, only each bank has double the cylinders and are alternately offset. This makes it look more like a 'W' head on, instead of a 'V'.

Hence 'W16'.

Each side of the engine has the exhausts separated into groups of four. Each manifold contains a turbo charger, giving it 4 turbochargers. Hence 'W16.4' name.