How does noise canceling headphones work?
First a short history lesson.
A guy named Amar Bose (the founder of Bose Corporation) was flying to Europe in 1978. During the flight the Jet engines was preventing him from enjoying audio in a pair of airline supplied headphones. Mr. Bose started immediately to calculate only to see if it was possible to use a pair of headphones as noise-reducing agent. Mr. Bose was introducing the first noise canceling headphones in 1988.
Ok now, How do they work and what can they do?
Sound waves have different wavelength and as any other wave, sound waves have crests and troughs. When two sound waves with the same wavelengths are in antiphase there will be cancellations. Noise cancellation headphones reduce unwanted atmospherical sound. For the noise canceling process, the headphones need a microphone and an electronic circuitry. The electric circuitry generates an antinoise sound wave with opposite polarity of the soundwave arriving to the microphone. This defeats the unwanted ambient sound.
The advantages with wireless Noise cancellation headphones:
You can enjoy audio without getting disturbed from noise in the background.
You can sleep better in noisy vehicles.
If you don’t have to raise the volume to hear the audio clear, your ears wont take damage.
Is there something more that you have to think about before buying?
One thing you should know is that they don’t eliminate noise entirely, They are preferable in airplanes, trains and other vehicles when not to much is going on in the background. Noise canceling wireless headphones have a lot of different shapes, the best thing to do is to go to the local reseller and try them out.
If you want to save a couple of bucks I recommend that you buy them on line.

Noise canceling headphones from Sony