Gain is the ratio of input voltage to output voltage. In the stock Quickie with a high load impedance, gain is about 2 - so for a 0.25 volt input, the output voltage is 0.50 volts. For an input of 1 volts, you get 2 volts output. Near the end of the battery life, the maximum output is around 2.3 volts RMS.
With a low impedance load, the gain and maximum output will be reduced. For a 10K load, the gain is about 1.7 and the maximum output at the end of battery life about 1.9v.
A "standard" CD player will generate a maximum voltage o2.0 volts RMS; that's sometimes called "full-scale" output, so 2.0vFS is a common abbreviation.
The gain control works by reducing the input voltage (e.g.2.0vFS from a CD player) to something smaller (e.g. 0.25v) which is then stepped up by the gain (i.e. 0.5v).
You can look in the specs to see what voltage a power amp needs to generate full output; it's usually around a volt but can vary a lot.
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Changing the subject a little - decibels are calculated from a voltage ratio, so gain can be expressed in decibels but voltage cannot. Voltage gain is 20 times the base-10 logarithm of the voltage ratio, so a gain of 2 is 6dB. To confuse the issue, the Powers That Be have invented the dBv, defined as the ratio of a voltage to 1.0 volts and expressed in decibels.. So 2.0 volts is 2.0dBv, while 0.5 volts is -6dBv.