Pinch harmonics are one of the most exciting and expressive sounds on the guitar. They can be used to add aggressive squeals to riffs and leads (think Billy Gibbons and Zakk Wylde) or produce different pitches off a single note for melodic application (a la Steve Vai and Eric Johnson).
Put simply, playing pinch harmonics involves a combination of the pick and the side of the picking hand thumb making almost simultaneous contact with a string during a down pick. There are many areas along a string that can produce a harmonic in this way, but they're commonly favored above the pickups which suits where the picking hand is naturally positioned when playing.
