A preamplifier (preamp), as its name suggests, is an amplifier which precedes another amplifier.
The second amplifier is typically a power amplifier (power amp). In this example, the job of the preamp is to amplify a low level signal, perhaps from a microphone or pickup, to line level and to apply any necessary equalization and tone control.
Originally, the mic and instrument preamps used in recording were built into the mix console; it was basically an "all in one" environment in which recording engineers placed their trust in the console builders.
This often means a tube preamp with a "warm" midrange (caused by slight harmonic distortion that's a normal part of tube operation) and "smooth" high frequencies (a result of mild low pass filtering caused again by the tubes' performance).
The reasons why one preamp would be more expensive than another are pretty much the same reasons one automobile is more costly than another; better parts, hand made, and sometimes, its desirability born of myth and legend.