Pre Amp processes the signal of the guitar to the right volume to be picked up by the power amp, and the power amp amplifies the signal.
I'm quoting D_Man here
Pre-amp. This is used to amplify the signal from your guitar a little bit before sending it on. This is necessary because pickups make a very weak signal and it has to be brought up to ?line level?, which is just the level of signal that is usually used for analogue audio signals (it varies a lot and I don?t want to get bogged down in electronics so I?m leaving it at that). EQ and much of the tonal character of a sound are applied at or around the preamp stage. Effects are also added at this stage, and headphones and line-outs come from the pre-amp.

Power amp. The pre amp sends the signal here. This is the part that does most of the amplification and drives the speakers.
PRS Standard SE
Laney GH100L with Marhsall 1960BV
Digitech Bad monkey
Marshall EH1
EHX Small stone
EHX Small clone