What is the purpose and function of a pre-amp in audio sound and production?

In general, a preamp simply takes a small signal and makes it larger.
In a guitar pedal, a preamp gives you more gain- easier to get some crunch.
A preamp can be at any level, short of a power amplifier that actually drives the loudspeaker. All guitar amps have preamps built into them. The signal from the guitar is fairly weak and can't drive the power amplifier directly- you would hardly hear anything at all. The preamp provides the missing gain, and in a guitar amp is what you are adjusting with the volume and tone controls.

I'm going to step way out of my depth here and also add that a passive pre-amp is basically just a system to switch between inputs and pass that signal on to the amp. No gain added. Is that correct?

GAIN IS at maximum, so a passive system "attenuates" the signal to the amp providing the source (a CD player) is passing enough signal to the power amp. I love preamps for two reasons- dubbing tapes where possible- a disappearing feature unfortunately, and precise control over the volume. This adds distortion, but frankly, I don't give a damn. I wouldn't even mind occasionally having/using a loudness switch, but only for crummy recordings. 
   BTW, some guitar pedals ("stomp-boxes") are truly amazing sounding and musicians can switch them on and off without stopping playing to adjust a rack-mounted preamp. They can be wired in series on a board and the tail end goes to the amplifier(s). Some guitars have gizmos inside to get different effects but need a 9 volt battery to power the circuits. 

GAIN IS at maximum, so a passive system "attenuates" the signal to the amp providing the source (a CD player) is passing enough signal to the power amp. I love preamps for two reasons- dubbing tapes where possible- a disappearing feature unfortunately, and precise control over the volume. This adds distortion, but frankly, I don't give a damn. I wouldn't even mind occasionally having/using a loudness switch, but only for crummy recordings.
   BTW, some guitar pedals ("stomp-boxes") are truly amazing sounding and musicians can switch them on and off without stopping playing to adjust a rack-mounted preamp. They can be wired in series on a board and the tail end goes to the amplifier(s). Some guitars have gizmos inside to get different effects but need a 9 volt battery to power the circuits.
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No gain added. Is that correct?

Not if you don't need to go any louder, it's not. There is no advantage being "able" to go to 11 but never doing it!

Cheers George

Let me re-phrase that last sentence a little.
" There is no advantage being "able" to go to 11 (ie: past full up) but never doing it, because "if" you did you’d blow your system up."

If it’s loud enough for you, you have enough gain, and better rotation on the volume control as well, instead of being stuck somewhere between 7o’clock and 10o’clock for your listening and never being able to use from 10 o’clock to 5 o’clock.

More gain DOES NOT! make a system sound better, if anything it’s worse as the noise comes up, as your chopping back (sacrificing) the source volume with the volume control just so the preamp gain stage can make it back up again, one should always use the "the full signal level" from the source if possible, this way noise is kept at a minimum.

EG: What the use of taking a Ferrari to redline in all gears, if your foot’s on the brake, knowing it’s not as fast or free revving if your foot wasn’t on the brake??.
That’s what your doing by reducing the source level a lot just so you can make it back up again with the extra gain of the preamp, why not just reduce the source level a little to where you need it? and not add more gain/noise/distortion.

Cheers George