A magnetic pickup consists of a permanent magnet with a core of material like alnico or ceramic, wrapped with a coil of several thousand turns of fine enameled copper wire. The vibration of the nearby lightly magnetic strings modulates the flux linking the coil, thereby inducing an alternating current through the coil of wire.
The coil - Insulated copper wire. Most common is a 42 gauge (40-49 gauge). The higher the number, the smaller the wire.
Insulation - Copper cannot be touching bare copper because it will short the circuit (enamel, poly nylon)
The bobin - The part that has the wire wrapped around it. A tall thin one puts the pole pieces close to the strings creating more upper mids and treble (Strats) Short and fatter ones (P90's, P-bass, or Jazzmaster) creates a thicker more powerful tone with more mids.
Ceramic: A clay-like blend of magnetic iron & rare earth elements that's formed into bars. Harder to magnetize but very stable once it is. It is bright with enhanced upper mids, hard and aggressive, compressed dynamics and punchy bass.
Alnico: An alloy comprised of aluminum, nickel and cobalt usually made into rods & bars. Easier to charge but less stable and can lose charge over time. They can sometimes be categorized in different numbers (alnico II or alnico V), this refers to the composition strength. The higher the number, the more cobalt (the stringer the magnet). The lower the number, the softer the magnetic fields (more sustain, softer sound, etc...)