How signal level is managed across the chain — source, preamp and power amp — so the system plays loud enough without noise or clipping.
Gain structure is the often-overlooked discipline of setting levels correctly through the chain so that each stage operates in its sweet spot. Too little gain and you can't reach satisfying volume; too much and you amplify noise or clip the input of the next stage. It's why a "low-powered" valve amp can be plenty loud on efficient speakers, and why a mismatch can leave a powerful amp sounding strained.
In practice it means matching source output, preamp gain and power-amp sensitivity to your speakers' sensitivity and your room. Get it right and a modest system sounds effortless; get it wrong and an expensive one sounds tense.