A Basic, Over-Simplified Definition of a Pickup
A pickup is a device (technically called a transducer) that "picks up" vibrations and translates them into an electrical current. Here's how it works, in over-simplified terms:
A pickup is composed of two things: a coil of insulated copper wire and a magnet. The magnet magnetizes the guitar strings. When the strings vibrate -- either through picking or strumming them -- the vibration causes the flux field of the magnet to move along with the strings. The motion of the flux field creates an alternating current within the pickup's coils. The alternating current then travels from the pickup, through the volume and tone controls, through the output jack, through the cable (or wireless) and finally to the amp where it comes out in the form of tone.