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