Forbes magazine recently compared two kinds of noise-reducing headphones as they might be used by business travelers. Noise cancelling headphones use microphones to listen to the incoming sound then a processing creates inverse waves which get fed back into the headphones. These inverse waves cancel out the ambient sound. One way to think about this is if the ambient noise (an airplane engine, say), is “+1” the headphones create and add “-1” so your ear hears 0 (i.e. nothing).