*realizes he could be getting played*
A muffler is part of the exhaust system of the car, the long skinny tubes where waste gases flow. Not quite sure of the British term for it (silencer?), but the part which is specifically called the muffler is the one which, when taken off the vehicle, results in very loud engine noises.
This is not to be confused with the muffler which is wrapped around one's neck, which, unless you have truly irritated your significant other, is made of cloth and designed to keep your neck warm. If you have irritated your SO, it may be the part from underneath the car...