The Amplifier

An amp's job is to take small electric signals and enlarge them. The amp must take the vibrations of the strings, which are a form of energy, and change them into an electrical charge, which is another form of energy. The electric charge is then sent through a transistor which opens and closes rapidly. This action allows the transistor to let out as little or as much as you dictate. The transistor acts as a valve which dictates how much of the electric current is sent to the speaker. This is how the amplification is achieved.

A somewhat simpler guide to amps: http://stereos.about.com/od/stereoscience/a/howampswork.htm
A very complex guide to amps: http://sound.westhost.com/amp-basics.htm