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.