Boston-based Bose is generally acknowledged as the leader in active noise cancelling headphones. In a nutshell, adaptive noise cancelling uses tiny microphones to listen to the world around the headset and then 'subtract' that noise from what you're hearing. The Beats Studio 3 are the only pair of noise-cancelling headphones Apple makes.
Apple calls their technology 'adaptive noise cancelling,' or ANC. The top feature on the Beats Studio 3 is noise cancellation.