Simplistic view: There are N different kinds of pre-amplifiers and M different kinds of power amplifiers. For an application, you can pick one of the N pre-amps and one of the M power amps, instead of having to find a combined unit that is one of M * N.
Think about pro audio for instance. There exist microphone pre-amps. A mixing board will have a whole bunch of them, one for each mic input. It would be silly to replicate that in a power amp. The power amp just gets the mixed result. In fact there may be more than one power amp. One for the "house", and a different one for local monitoring.
A microphone pre-amp is a different beast from, say, a guitar pre-amp, etc.
Why would a guitarist want a separate pre-amp and power amp? Well, not all do. There are "combo" amplifier that have a preamp, power amp and speaker cabinet all in one. (And there have been electric guitars with a built in speaker, yielding complete integration.)
But having separate units in a rack: pre-amp, equalizer, effects processor, power amp, gives you flexibility.. Don't like how the power-amp drives the speakers? Swap it out; see how the setup sounds with a different one. You can change one "variable" at a time in search of tone.