The principle behind Electronic Ambient Noise Cancellation (ANC) is to detect ambient noise around the noise-cancelling device and create an “inverse” noise signal to reduce or eliminate the ambient noise to whatever extent possible. There are two different approaches to ANC in headphone design - “Feedback” and “Feedforward”.
The “Feedback” method is based upon a closed-back, circumaural (ear-surrounding)-type headphone system. This system is good at cancelling low-frequency noise, but the wearer ends up feeling isolated in their environment as this method eliminates a very large percentage of background noise.
The “Feedforward” method does’t require a tight seal around the ear, and consequently doesn’t require large, bulky earmuffs. The wearer is able to hear his or her environment, providing a more natural user experience. Feedforward is well suited to mobile device applications.
You can find more ANC technical information here.