The idea behind humbuckers is to use two separate pickup coils, each wound in a different direction, over a central magnet. The hum is cancelled out by the two different coil directions (hence the name 'hum-bucker'), and the overall tone is generally thicker, louder, warmer and fuller than single coils. Humbuckers are great for heavier styles like classic rock, hard rock and metal, and they can add some toughness and raunch to blues too. And the softer, smoother tone of humbuckers makes them great for jazz as well, especially if you use a humbucker in the neck position on a big hollow-body guitar. Gibson guitars are closely associated with the humbucker as their iconic models, such as the Les Paul, SG, and ES-335, all use them. Bare Knuckle, Fishman, EMG, Seymour Duncan and more all make humbuckers ranging from vintage-style, to high-gain metal monsters.
In some cases, you'll see single coils and humbuckers in the same guitar. Popular configurations include a humbucker in the bridge position with single coils in the middle and neck spots, humbuckers in the bridge and neck with a single in the middle, or a single coil in the bridge position of a Telecaster with a humbucker in the neck position.