How noise cancelling works, in general
Noise cancelling earbuds listen to the sound around the wearer and produce a counter-sound that reduces it. It works best on steady, low sounds — engine hum, air conditioning, office drone — and less well on sudden, sharp sounds. A good seal in the ear matters as much as the electronics: sound that leaks past the bud cannot be cancelled.
Where buyers use them
Common uses are travel, open offices, and sleep — the last one is a distinct use, because a bud worn in bed must be small and comfortable on its side. Sleep use, travel use and office use are different requirements, and an inquiry should say which one is intended.
What to confirm before ordering
Ask how the cancelling behaves with the seal broken, what happens when the battery runs out, and whether the buds still play audio passively. Do not accept a single decibel figure as the whole story: the figure depends on the test conditions, so ask for the test basis too.