From my reply to a discussion in r/guitarpedals on Reddit.

A preamp pedal is very simply a pedal that amplifies your signal at the start of the signal chain. Because it makes your guitar signal louder, it affects how the guitar sounds both with other pedals that come after the preamp, as well as the actual guitar amplifier. There are a lot of reasons you might want to use a preamp pedal, but ultimately it comes down to liking the way it makes your rig sound.

By way of example, you probably already know that adjusting the volume knob on your guitar will change the sound coming out of the amp. Now what if you could keep making your signal louder when your guitar volume knob was maxed out? Turns out you can, with a preamp.

You can get a sense with how this works, if you have an EQ, boost, or even a distortion pedal that stays clean at lower gain settings. Put it at the beginning of your signal chain, connected immediately into your guitar, and then see what happens when you engage it. You may notice your later distortion pedals sound more driven, or your amp is pushed further into overdrive. If you like that effect, a preamp may be for you.

Then you get to dive down the rabbit hole of what different preamps can do, because in addition to volume, they usually also have tonal controls. With that, a preamp can be very useful in getting solos that cut through a mix, or taking the mud out of your rhythm playing.