How Do Noise-Canceling Headphones Work?

You’re on a flight, and the drone of the engines is getting on your nerves, so you pop on a pair of noise-canceling headphones, and sweet, blessed silence descends. But those headphones aren’t just muffling the sound — they’re actually making it go away!

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Sources:
http://electronics.howstuffworks.com/gadgets/audio-music/noise-canceling-headphone3.htm
http://mentalfloss.com/article/49988/how-do-noise-canceling-headphones-work
http://www.phys.uconn.edu/~gibson/Notes/Section5_2/Sec5_2.htm
https://thetartan.org/2010/2/8/scitech/noisecanceling