A great many confuse "gain" with distortion. The tonal consequence of increments to gain, however, depends on context. So the amount of gain applied to a voice mic, to get a nice clean-but-hot signal to maximize S/N ratio, is often well in excess of the amount of gain applied to a guitar that would send an amp into clipping. But that's because a) a voice mic starts out as a much lower-amplitude signal than a guitar, and b) the mixer or mic preamp is designed to apply gain cleanly, with lots of headroom, where a guitar amp applies additional gain, internally, and is designed to anticipate a signal only a bit hotter than a slightly boosted guitar.
dtsaudio nailed the definition nice and clearly. I would only add to it that what is often referred to as a "buffer" generally has a gain of 1, where Vin = Vout. That is, no amplification is applied. At the same time, because the buffering action will prevent against potential loss of higher-frequency content, buffers can result in an audio output that sounds "louder" because less top end was lost. Still, no gain. Weird, huh? No shame in being mystified by it.