Because I live under a rock, today I decided to look into what a “Noise Cancelling Headset” does. I had no clue and thought it was some sort of gimmick …
Wiki: “They incorporate a microphone that measures ambient sound, generate a waveform that is the exact negative of the ambient sound, and mix it with any audio signal the listener desires.”
This sounds like witchcraft to me. 
Does it actually work?
Is it this expensive? …
Yes it works. I even have shooting ear pro that works in a somewhat similar fashion. It allows you to hear normally, and then cuts off with loud noises (gun shots). Pretty sweet stuff.
That depends really on the properties of the noise.
For low frequency stationary noise (that means that the properties of the noise remain somewhat constant) it does work quite well (e.g. GA prop noise). Cancelling nonstationary signals like speech is technically very difficult. You can expect the sophistication of signal processing to vary wildly from low to high end models.
Because cancellation at higher frequencies is damn near impossible, the active cancellation should be compounded by passive dampening (which incidentally works much better at high frequencies than at lower ones).
It is usually a good idea to try the headphones out in the environment you are going to use them in to see if they cope well.
We use the Bose A20 in out turboprops, and they are great! The difference with noise cancelling on or off, is huge!
Like @sobek mentions, they are better suited for cancelling a constant steady frequency. For cockpit use, that means they cancel engine, propeller and wind noise, but allow for warning and alert signals to be heard.
Noise cancelling is also used in many aircraft cabins as well. The cabin walls are lined with microphones and speakers, that pick up the noise and cancel it. Now, as you may imagine, it looks better on paper than it does in reality. Especially when one, or a few, of the microphones drops out, and the system goes out of synch… Instead of a negative wave form that cancels the noise, you may get an out of sych wave form that enhance the noise, at certain intervals. Sounds like loud pops. Usually scaring the crap out of some poor passenger… 
How do i put this delicately? This is only ‘sort of’ what i said. 
It is not important for the function of the ANC whether the signal only consists of one frequency or, as is typical in real life noise processes, many frequencies. If we’re being exact, the noise needs to be quasi-stationary, that means that its properties change only very slowly (so slow that the control circuit can estimate the changed signal way before the properties change again).
Yes. I was just trying to explain why noise cancelling works so well in an aircraft.
I’m sorry if you feel I was paraphrasing out of context.
Noise-cancelling headsets are indeed witchcraft - or they work well enough that they might as well be.
The following has happened around me, which is kind of funny:
A couple of years ago, I had a friend from France come live at my place for a couple of months. He had just flown over and raved to me about these noise-cancelling headphones he bought and how great they were on the long-haul flight.
I tried them out.
Holy crap - it was as though someone suddenly turned off your ears.
I had a trip to Finland coming up so I got the then-latest Bose’s (QuietComfort 25) from the duty free and absolutely loved them.
I continued to use them at work, as they work superbly well in an open-plan office, cancelling out aircon hum completely and dampening conversations around you well enough that you can concentrate a lot easier.
A few months later they started demolishing a big office block right next to my wife’s work - so she borrowed my headphones to close out the construction noise. Her colleagues tried them out, loved them and now the whole floor has the same ones (I ended up buying her a pair of her own).
And now…the same thing has started to happen in my office, there’s already four other users and more people are considering it, haha. What’s annoying to me is that the next model up (QuietComfort 35) has come down in price so all these noobs have nicer, Bluetooth versions than my original gangster model!
So yeah - Bose should really send me a free pair as I’ve directly or indirectly given them a fair amount of business, haha!
Pulling the cable makes the noise cancel on my headset
These are mine…
Strangely my work slow down considerably when they are active…
I bought some way-too-expensive Bose Quietcomfort 2 headphones 7 years ago when I was commuting to Seattle for 6 mos on the Delta night coach. My wife was stuck out there with our first child in the NICU, because our daughter decided to be born 16 weeks early! Anyway, since we were footing the bill, I was crammed in economy and the max density that Delta could pack into B752, without headrest monitors. If the person in front of me put their seat back, it hit my knees and covered the tray table.
Anyway, that $350 that I spent in the SEATAC Bose store one night after a couple of beers, was one of the best investments I’ve ever made. They turn a miserable trip into tolerable. And I use them now when on road trips with the family. The kids will be watching Frozen for the 867th time while I listen to the Fighter Pilot podcast or an audible book while chaos reigns behind me.
These are mine, I guess not as fancy as the Bose but it works well!
What about all those poor pedestrians that have to listen to your terrible noise
Eeh, they’ll manage! Got a EU approved exhaust on it for noise abatement and the plugs are more for wind then engine noise. Once you go above 80km’h there’s not much hope of hearing a lot from your engine!