Noise cancellation headphones, whilst becoming increasingly common, are still poorly understood. The basic concept that anti-sound is created to neutralise incoming noise is not wrong but it really leaves more questions than answers.
A product that claims to have noise cancellation may or may not offer a real benefit to the user. Why is this? The noise cancellation system aims to create “anti-noise” to reduce the apparent noise level at the ear, however an inevitable consequence of creating the anti-noise is that some frequencies will also be boosted in level. If the noise cancellation is designed poorly the added noise will be worse or equal to the noise reduction, in which case the design has failed. The user may hear a “difference” when the noise cancellation is switched on, but that difference doesn’t necessarily mean the noise cancellation is a net benefit. With careful design the added noise will be insignificant and the user will benefit from a quieter environment. Many producers take advantage of the consumers limited understanding of noise cancellation to sell products that claim to have noise cancellation (along with vague claims of dB reduction or % reduction) when in fact the end user doesn’t really get the benefit they expected.