Preamp

Preamp is short for preamplifier.  As the name suggests, it is used to amplify a weak signal to a desire level before any other signal processing. 

With microphones, the preamp is to bring the low mic level up to a line level.  With guitar amplifiers, there are preamp and power amp sections.  The preamp helps to boost the guitar signal, very often adding colour in the process, before going into the power stage for more loudness.  This is exactly what a preamp pedal is for.

Preamp pedals are often designed to emulate the preamp section of a guitar amplifier.  Use it to add colour to your tone or simply add gain to your signal to push your power amp to produce the overdriven tone.