In the idea of unity gain, the input and the output between two devices are the same level. That's to say, when a microphone is outputting 0db, a mixer will also be outputting 0db worth of signal. Unity gain is established by calibrating two pieces of equipment to talk at the same level.
Frequently, the best way to set unity gain is to adjust a microphone or line signal gain to 0db, measured both at the preamp and output stage, and then match that 0db level simultaneously on the input of the second piece of equipment -- whether an amplifier, recording software, or mixer.
Unity gain is useful for several reasons. First, it gives significantly cleaner and non-distorted signal. Microphones will sound much fuller and with much better dynamic range. There will also be a much easier time applying outboard effects, as most effects units are set to accept a unity signal.
If you're mixing sound live, getting proper gain staging is important. You'll also nearly eliminate major feedback problems, as a proper unity gain allows optimal gain-before-feedback. Keep in mind, the more gain you can get cleanly and without distortion, the better your mixes will sound!