A preamp is a tone shaping tool and a signal booster. For guitar purposes, a guitar amp can be separated into 3 different components... the preamp, poweramp, and speakers. The preamp is where you adjust the eq, dial in overdrive/distortion, and generally shape your tone. The preamp sends the signal to the power amp. If it is a tube amp, the power tubes will also add some coloration to the overall sound. From there, the power amp send the signal and power to the speakers, which produce the sound you hear.

For recording purposes, a preamp can be used for several different applications. The two main uses are to booste the signal of a mic, and to add warmth and presence. Look at it like this way... If you plug a mic (SM57 for example) straight into your recording device, it will sound kinda dull. If you pug it into a preamp the sound will become fuller and more lively, and generally better.

I'm sure there are better, and more in depth explanations, but that should give you an idea.