...to complete the picture...
Although all basically correct, I think Bobbsy's explanation is the most technically clear and accurate. However, even though a preamp can be understood in simple terms of voltage alone - what's commonly called "signal level" - that's only part of the story.
OK, now if you're in a hurry it's OK to jump to “Here's all you need to know” below.
For just the brave souls...
Besides voltage, any analog audio circuit (or any electric circuit at all, for that matter) also has three other important aspects:
Power, expressed in Watts and designated with the letter P or W.
Current, expressed in Amperes or Amps and designated with the letter A.
and Impedance - or "AC Resistance" - expressed in Ohms (sometimes symbolized by the Greek letter "Omega" which looks like a horseshoe open on the bottom), it is also sometimes designated with the letter Z.
To complicate matters further, Impedance is often confused with a fifth aspect: DC Resistance. Although expressed in Ohms like Impedance, DC Resistance is only used for describing pure DC circuits.
So, how can any sense be made of all this? I've personally had good luck with simplifying it to just two of the five parameters - Voltage and Impedance. You can usually ignore the other three (Power, Current, and DC Resistance) without suffering too many problems in selecting gear. Power was critical in the old days because of primitive circuit techniques, but it's usually important now only when dealing with power amps and speakers. As for DC Resistance, that can be ignored because all audio is by nature AC (Alternating Current; Note: don't let the word "Current" throw you. Here Current implies the four other terms; except (as noted above) sometimes for pure DC circuits, none of them can exist without all the others).
So how does this help us understand mics and preamps?
Here's all you need to know:
About the mic you want to use:
1. The sensitivity spec given for the mic in decibels (-dB). Keep in mind that the bigger the sensitivity number the quieter the sound you can pick up with that mic.
2. The mic's Output Impedance in Ohms.
About the preamp that will work for that mic:
1. Check that it has a maximum Voltage Gain in the ballpark of the mic's sensitivity, say, plus or minus 10dB. Taking for example a mic sensitivity of -60dB, you'd want preamp max gain in the range of 50 to 70dB.
2. Check that its Input Impedance is in the range of the mic's Output Impedance AT THE VERY LEAST, to up to five or six times the mic's Output Impedance. So, for a mic Output Impedance of 300 Ohms, you'd want the preamp's Input Impedance to be in the range of 300 to 1,000 or even 2,000 Ohms. Note that some of the more sophisticated preamps actually have a variable Input Impedance or “loading” control that can be used to “tune in” a certain coloration of sound.
See – nothing to it!