In terms of the physics, it just plays sound out of phase.
I think this means that it literally physically cancels the vibration.
However, I'm suggesting that there may be a problem if it doesn't get the timing right. To cancel a noise the ANC has to mimic it, out of phase with the original noise. If it's not perfect you get a sound artefact. That's why you get hissing in the background,
Ive noticed that if I push my NS1000s tight onto my ears and then let go, there's sometimes a squeeking sound. I interpret this as air rushing past the microphone used by the ANC circuit and that playing the sound out of phase.
The thing was - the air rushing past was very loud to the internal mic. You'd barely hear it and the resultant sound produced by the ANR is very much out of proportion to what makes it to your ears from the original noise.
I wouldn't have thought it would be a problem for normal use but I don't think it's sensible to use ANC headphones as ear defenders in a noisy environment.