In simple terms, it's when an "amplification device" (it's usually pre amps) doesn't provide voltage gain, but just sources the current needed into low input impedance loads. This is otherwise known as a buffer. I used the word amplification in quotartion marks as there's no amplification of voltage taking place in such devices. Voltage going in is equal to the voltage going out, thus the unity gain name.
Most such preamps do have a volume control to attenuate the voltage for lower listen levels but they will pass all the voltage from the source such as a CD player, along with more current (as needed) to the amp when the volume pot is fully opened.