Electronic Ambient Noise-Cancellation (ANC) principle is to detect the ambiment noise and create a “inverse” noise signal to reduce or destruct the noise to preceive noise level. There are two different approaches in heaphone design - “Feedback” and “Feedforward”.
“Feedback” method is based upon a closed-back, circumaural-type headphone system. This system is good at cancelling low-frequency noise, but feeling isolated in the environment.
“Feedforward” method does not require a well-sealed cavity design around the ear. It is able to hear the environment and provide a more natural user experience. It is good at a mobile device application.
You can find more ANC technical information here.