When you record sound with a microphone, a microphone preamp is needed to boost the signal so it's high enough to actually be recorded. The preamp is connected to the gain control found at the input stage of a mixing desk or an audio interface.
Preamps are often misunderstood, but they're actually simple to understand. When sound energy gets converted to electrical energy inside the microphone, the electrical signal that's generated isn't strong enough to be processed any further. The preamplifier (preamp for short) boosts the signal so it can be used in mixing desks and other audio processors and devices.
Without preamps, we wouldn't be able to record anything usable from our microphones. I think you'll agree that they're vitally important to what we do in our studios.
You'll find a microphone preamp at the mic-level input stage (the XLR input connection) of each input channel on both analog and digital mixing desks. Sound cards and audio interfaces also have mic preamps built into them for each XLR input.
The two most important elements in the studio that affect the tonal quality of your recordings are the microphone and the preamplifier. Each mic has it's own characteristics, and it's the most important part in the signal chain that can affect the 'color' of your recording. But the preamp can also have an influence on the recorded sound's characteristics.
This is why you can also get outboard preamps, that can bypass the preamps found in mixing desks or sound cards. Some sound engineers and producers I know all have their favorite preamps that they use over and over again, and most of them have familiar mic/preamp combinations that give them the specific tonal qualities that they're after for a particular recording.
But to really notice these sorts of tonal differences you would probably need to purchase a preamp that was in the high-end range, which can be quite expensive. High-end devices like these are often referred to as 'Class A' tube mic preamplifiers.
Cheaper preamps don't really add enough of a difference to your recorded sound to justify the cost of buying one. There're many other ways you can adjust and change the qualities of a recording, such as choice of microphone, mic setup and positioning, mic technique, or better gain control at the recording stage.
Outboard devices usually have other features as well, such as phantom power for condenser mics, hi-pass filters to help remove low frequency hums and vibrations, and monitor/headphone mix outputs. You'll normally find these features on mixing desks and sound cards as well.
As I've already mentioned, it's probably not worth purchasing a dedicated preamp when you're at the beginning stages of setting up your home studio. You can still get good results from the inbuilt preamps found in a mixing board or a sound card.
But if you have some extra money handy and you'd like to further improve the quality of your recordings, then it won't do you any harm to look into the possibilities that a microphone preamp can bring.