What is a guitar pickup?
Definition of a guitar pickup
To grossly over-simplify, guitar pickups are permanent magnets that are coiled with copper embedded underneath the guitar strings on your guitar. These coiled magnets create a magnetic field which then detects disturbances in the movements of the strings and transfers that signal to an amp.
If your eyes are glazing over, I empathize. Seriously, I do.
How guitar pickups work
Coiling a magnet, to bring you kicking-and-screaming back to fifth-grade science, creates a magnetic field. When that magnetic field gets disturbed, like if you strummed a G chord, the sound is "picked up" by the guitar pickup. Then, the disturbance is transformed into an electric signal, and then brought to an amp (and preferably a loud one).
The electrical output of a typical guitar pickup is nothing crazy. If you're wondering, you can't get electrocuted by putting your hand on a guitar pickup. That said, it's a terrible idea to take a bath and play electric guitar while it's plugged into an amp. That could be electro-nasty.
The most common type of guitar pickups out there are magnetic. Pickups most commonly come in two basic forms: humbuckers and single coils (acoustic-electric guitars come with sneaky, hidden pickups called piezo pickups). You can certainly find more unique pickups, and you can definitely find guitar pickups that are completely crazy, like lasers.
Images of the two most common guitar pickups
Humbuckers
Electric-Guitar-Humbucker-Pickup, by Dave Wirth
Single coils
Single-Coil-Pickup by Dave Wirth