Wikipedia (www.wikipedia.org) states, noise cancelling is a method for preventing unwanted sound. Sound consists of vibrations in the air, which can be represented as a wave. If a speaker emits a sound whose wave has the same amplitude and the exact opposite polarity to the original sound, the waves cancel out and the result is no sound at all.

While this seems rather technical here is a more simple explanation: sound waves are created by the noise cancelling headphones to counter and eliminate the unwanted sound waves outside of the headphones or speakers. A digital signal processor determines what sound wave is needed to cancel the outside sound wave and it produces that sound and amplifies it through the headphones.

This method differs from noise-reduction headphones which are designed to reduce the noise you hear by physically blocking the sound from reaching your eardrum. This is the same passive, unpowered method that is used by insulation or sound-absorbing ceiling tiles in your home.

Noise canceling headphones tend to work best for constant sounds like lawn mowers and appliances but they allow in intermittent sounds, such as conversation or a ringing phone, so you are not totally isolated. They are also known to be more comfortable than noise-reduction headphones since they are lighter weight and generally smaller in size than noise-reduction headphones.

Some of advantages of noise cancelling methods compared to noise-reduction methods are:
They can be more effective at low frequencies
They can be less bulky
They can be selective in that they can block noise (e.g. from an engine) but not useful sounds (e.g. voices).

Some of disadvantages of noise cancelling methods compared to noise-reduction methods are:
They consume power, usually supplied by batteries that must be replaced. If the batteries die the noise cancellation stops working; and if you are using the headphones to listen to music, in many models, the music stops as well.
They may introduce additional noise, usually in the form of high-frequency hiss. Noise cancellation headphones attempt to block sound by sampling the outside sound and then producing an equal but opposite sound sometimes the approximation of sound can be difficult.

Whatever method of noise reduction you choose, it can help prevent hearing loss. By using headphones when listening to music, you can hear the music at much lower volumes because you are not trying to drown out background sounds. And those around you wont have to listen to your music; it can be contained in the headphones.