What actually is a preamp?

"Preamp" as a technical term, to the extent that it even is a technical term, is an amplifier stage that adds enough gain to bring the signal up to "nominal level," which basically means a level you can work with. It often includes impedance conversion to account for outboard sources of unknown impedance. If you look at the numbers on the gain control of a Neve 1073, it shows what level the input signal should be vs. 0dB to achieve 0dB at the preamp output. The goal, according to the preamp, is to lift incoming signals up to 0dB so they can be mixed together or worked with in some other way. After the preamp, processing ideally is net 0dB up to the mix fader. This allows for lowest noise, highest headroom, and lots of other good things. Of course, in practice this is an ideal we can't always achieve, but it's good to understand the ideal.

As it relates to guitar and guitar pedals - A guitar can't drive a power amp directly, because the level is way below "nominal," so the earliest "guitar amps" are a simple single-tube preamp added to the power amp of a typical radio of that day. So a "guitar amp" has a preamp and a power amp section in it - but in the world of effects pedals you're putting processing before the preamp, which is counterintuitive from an engineering perspective but makes total sense in practice. The pedalboard becomes a prepreamp, and then some pedals call themselves preamps which would make them preprepreamps... This helps us realize that these terms are more about use-case and don't necessarily have a strict meaning technically. You can call a boost pedal a preamp if you want, if you are using it that way. In context, the whole pedalboard can be thought of as a modular channel strip, with an input driver, preamp stage, signal processing, and an output driver.