While you are traveling in an airplane or sitting beside a busy street, the ambient noise makes it difficult to enjoy listening to music from headphones. You may have to turn up the volume to unbearable levels in order to hear all the sounds. This takes away from the enjoyment. For this reason, Noise-Canceling headphones have been developed. What they do is that they actively cancel out the external noise so that what you hear is only the music.
The headphones have a microphone attached to some electronic circuitry. When the mic detects a sound, the electronic circuit produces a wave that is in the exact opposite phase of the one detected by the mic. This leads to destructive interference and negates the external noise. This technique is only effective for low frequency noise, like the hum of refrigerator or airplane, so traditional sound-proofing techniques are employed to cut the high frequency noise.
Noise canceling headphones are made by most notable headphone-makers with the most prominent player being Bose.