What’s the relationship between gain (dB) and power (watts)?

Very simplified electrical info following:
One can think of voltage as electrical pressure (or potential force), resistance somewhat like a valve that restricts flow, and amperage as the physical amount of electron flow, for the sake of a simplified analogy.

Electrical work (measured in Watts) can be calculated many ways, a simple one is the amount of electrical pressure (Volts) multiplied by the amount of electron flow (Amperes).

As nitroxpro states, that it is an exotic alternating current, I would say for simplification that it also meets an exotic resistance (impedance curve).

Amplification can be somewhat described as if you had a small electrical signal controlling a valve on a larger electrical signal, as the smaller signal swings from positive to negative, in higher and lower amplitude from zero, it opens and closes the valve proportionally, positive and negative.

The amount higher than the source signal the amplifier potential has, could be considered gain.
Now it takes a certain amount of power to meter the valve (like in a tap), there is the impedance and the voltage of the AC coming in, if it's too little it won't open the amplifiers (tap so to speak) to realise it's maximum output.

The maximum output potential of the second amplified signal can be considered it's available working power.
Even if you hold the tap wide open, it can't possibly feed more power than is available, than the potential electrical pressure the amplifier can produce, through that valve.

I say there is exotic resistance because the components of the crossovers, the windings on the drivers are reactive to different frequencies, this reactive quality can be measured as impedance curve.

https://www.audioholics.com/loudspeaker-design/understanding-impedance-electrical-phase/page-2

Resistance is the term used to denote the opposition to the flow of current in a circuit or material. It depends on the resistivity and dimensions of the material. The resistance offered by a material to the flow of direct current and alternating current remains the same. It is denoted by the letter R.

Impedance

Impedance is the opposition to alternating current. It is a combination of resistance and reactance. It is represented by a complex number and has a real and an imaginary part. The real part represents resistance and the imaginary part represents the reactance. Reactance can be capacitive, reactive or a combination of both.

source: https://www.electricalclassroom.com/resistance-vs-impedance/

@rixthetrick - thank you sir!  Love your posts and will refer to them again as needed.

Amplification can be somewhat described as if you had a small electrical signal controlling a valve on a larger electrical signal, as the smaller signal swings from positive to negative, in higher and lower amplitude from zero, it opens and closes the valve proportionally, positive and negative. 

This is where my technical ignorance seems significant.  Maybe I’d need a textbook to understand this:


Well, think about how much an amp can do.  Amps can't have infinite power, or output voltage, right?  They are limited devices.  Every one of them. What limits them?  Among many things, the voltage available to the output circuits. That is the absolute limit of output.

Your gain is 20x (28 dB) for instance.  OK, but your maximum voltage out is 10 Volts peak to peak.

1 volt pk-pk in x 20 = 20 Volts pk-pk. 

With this amp, 20 volts out is not possible.   You need a bigger amp.  What you'll get instead is a clipped signal that goes up to 10 and hangs there until the input voltage goes back down.