When two identical waves meet, they add. In phase they reinforce each other; half a period apart they cancel. Try it first with two sine tones, then with a full music loop and its polarity-inverted copy, and listen to how fragile perfect cancellation is. Press Start audio first.
What to notice: perfect cancellation needs identical, perfectly aligned signals. A few milliseconds of misalignment gives colouration, not silence, which is why noise-cancelling headphones must react so quickly and why the trick rarely works out in ordinary rooms.