What is active / passive noise reduction pilot headset?
An active noise cancellation pilot headset system reduces unwanted noise by creating a signal identical to noise but exactly reversed in phase. The effect of that signal is noise cancellation. As a part of this system, there is a small microphone inside the headset, which receives noise, which we could hear, without that system. Then some electronic system creates an anti-noise signal which cancels intruding noise.
A quality pilot headset with active noise reduction system is usually priced around €1000. Example of such headset is popular Bose A20 or David Clark DC ONE-X.
Passive noise reduction is nothing but ear cups designed to reduce unwanted noise from the outside. Cheaper pilot headset usually comes with passive noise reduction only.