What is the definition and purpose of a pre-amplifier?
There are many reasons why you would want a pre-amp and a power amp. The easiest to understand is when your source and destination are far away from each other. In this situation a pre-amp can be helpful so that the noise that is picked up on the line to the power amp is minimal compared to the signal itself.

Another situation is if you were going to be performing some filtering on a signal. All of the filtering elements can add noise to your system and by adding a preamp the noise in the filtering is minimized compared to the signal. Also the preamp can act as a simple buffer between your source and the filtering equipment.

And yet another reason you would want it is because your preamp isn't able to provide the current gain required for the power amp. You may still wonder why not just use a power amp? Power amps are more difficult to directly change the volume on while a preamp is much easier. So you can change your volume on the preamp and have a fixed gain on the power amp.