The pick-up is important in the chain that generates the final sound for the electric guitar. Lets look at how it works. The term transducer, which is an electronic or electromagnetic device that converts physical energy into electric energy, is well adapted to the pick-up. This, in fact, converts the energy produced by the vibration of the strings into alternating current (AC) electric impulses, which are then directed to the amplifier, that manipulates the signal that is then sent to the cones of the speakers, whose characteristics we hear in the form of physical sound. The pick-up of an electric guitar is usually magnetic, in the sense that it is made of a magnet with the function of creating a magnetic field inside of where the strings pass. In fact, the pick-up only functions near the strings, and is therefore mounted directly below them.
There are two fundamental catagories of pick-ups: the single-coil pick-up and the humbucking pick-up, with their variations (active and splittabile pick-up's).

The pick-up basically is a fixed bar magnet that is wrapped with very fine copper wire (the dimension of a human hair). The wire is wrapped around the bar many thousands of times, creating an electrical coil. The magnet of the coil generates a magnetic field around itself and the strings of the guitar, when the pick-up is mounted just below. When the strings are stopped, the magnetic field is inert. When the string vibrates, the form of the magnetic field is altered.

The internal magnetic bar of the pick-up. Copper wire is wrapped around the central part.