How does a pre-amplifier work and why is it needed?
Generalizing, power amps for audio devices all tend to have the same input characteristics to make them compatible and generally interchangeable. Pre amps tend to have an output level and impedance compatible with power amp inputs BUT, a pre amp is usually specific to it's signal source and you'll find that a pre amp suitable for a guitar is not suited for a microphone. 

Within the microphone family there are many different types and a pre amp suited for an electric or condenser Mic will be pretty poor with a ribbon Mic and some moving coil microphones.

Pre amps also tend to incorporate tone controls and these tone controls are clearly just affecting the instrument that is plugged in whereas the tone control of a power amp (when it receives signals from a mixing desk) will make global tonal changes to all the instruments.

As mentioned in another answer, pre amps tend to have very low noise inputs, making them suitable for signals that are particularly weak. Pre amps can also feed phantom power to condenser microphones.

In short, pre amps are tailored to the specific instrument that they are intended for and another example is the pre amp for a moving coil pick up cartridge on a record deck. It has a specific frequency characteristic that de emphasizes the cartridge's incorrect characteristic thus making it "sound" correct.

Perhaps an analogy with a different industry will help. Think industrial sensors and data collection. This sort of system might use an ADC to digitize signals from various sensors but each sensor will require a different pre amp to feed to the common ADC. In this rather weak and off-the-cuff analogy, the input to the ADC can be thought of as the "standard" input to a power amp. Inputs can vary more so than in the audio world. 

For instance, a thermocouple has a very low level output and may require large amplification but, it's bandwidth is usually small so low noise amplifiers may not be needed. A strain gauge can also have a low level signal but can be used up to many tens of kHz and can need very specialist pre amps and activation with a polarization current. RTDs tend to need low gain and most applications are limited bandwidth. Horses for courses.