Noise cancellation is the phenomena of cancelling or muting the unwanted noise of the background to have a better experience while enjoying content on headphones.

The discovery of noise cancellation was done by Paul Lueg in the year 1933, he realised that he could cancel sounds of a loudspeaker by using phase advancing waves, which causes interference with the sound produced by loud speaker.

This discovery led to the Active noise cancellation we know of today.

https://hammeronline.in/blogs/post/how-do-noise-cancelling-headphones-work-pnc-anc