They use an adaptive finite impulse response filter where all the
filter coefficients can be varied.
Once adaptation has completed the filter has an impulse
response which is the complement of the impulse response of the
speaker + room + microphone. If something changes, like a person
moving around, there will be a slight echo that gradually
disappears as re-adaptation takes place.
The filter needs enough taps to delay the audio by a time corresponding
to the reverberation time of the room in order to get "complete"
cancellation.
John