The development is a special case of the differential microphone topology most commonly used to achieve directionality.
The microphone's proximity effect is adjusted so that flat frequency response is achieved for sound sources very close to the front of the mic – typically 1 to 3 cm.
Thus if one signal is subtracted from the other (in the simplest sense, by connecting the microphones out of phase) much of the noise is canceled while the desired sound is retained.
Other techniques may be used as well, such as using a directional primary mic, to maximize the difference between the two signals and make the cancellation easier to do.
The internal electronic circuitry of an active noise-canceling mic attempts to subtract noise signal from the primary microphone.