A humbucking pickup, or humbucker is a type of electric guitar pickup that uses two coils to "buck the hum" (or cancel out the interference), induced by the alternating current in single coil pickups. All pickups use magnets to produce a magnetic field around the strings, and induce an electrical current in the coils as the strings vibrate. Humbuckers work by pairing a coil with the north poles of its magnets oriented "up", (or toward the strings), with a coil which has the south pole of its magnets oriented up. By connecting the coils in series and out of phase, noise and interference are significantly reduced via common-mode rejection.
Hum is caused by the alternating magnetic fields created by transformers and power supplies inside electrical equipment using alternating current. While playing a guitar without humbuckers, a musician would hear a slight but significant hum through their pickups during quiet sections of music. Sources of studio and stage hum include high-power amps, processors, mixers, motors, power lines, and other equipment. Compared to single coil pickups, humbuckers dramatically reduce hum, and produce higher output, because both coils are connected in series. They do result in a different "tone" from single coil pickups.
Read more about Humbucker: History, How Humbuckers Work, Notable Humbucker Designs, Other Noise-reducing Pickup Designs