"Noise-cancelling" gets used loosely, but there are really two different things happening inside a good pair of headphones. Passive isolation is just physics — a snug ear cup or eartip physically blocks sound waves from reaching your ear, the same way earplugs do. Active noise cancellation (ANC) is the clever part: tiny microphones on the outside of the headphones listen to the ambient noise around you, a processor generates a sound wave that's the exact inverse of it, and the driver plays that inverse wave through your ear canal. The two waveforms cancel each other out, and what's left is silence — or close to it.
ANC is especially effective against constant, low-frequency noise like an airplane engine's drone or an HVAC system's hum. It's much weaker against sudden, high-frequency sounds like a dog bark or a dropped tray table, since the processor can't predict and cancel something it hasn't "heard" yet. That's why the best headphones combine strong ANC with a genuinely good physical seal — the electronics and the foam are doing two different jobs.
