When you're in the bath, you can push the water in one direction to make a wave. A wave has a point where the water is highest, the peak. And a point where the water is lowest, the trough. If you have two waves in the same body of water, they can overlap. When the peaks overlap, you end up with an even bigger peak. But when a peak overlaps with a trough, they cancel each other out.

Active noise cancelling works in the same way, but with sound waves instead of water waves. A microphone picks up the sound you're hearing from outside, and the speakers make the opposite sounds at exactly the right time to cancel them out.