It’s complicated math, and pretty dependent on the actual circuitry and specific type of amplifier.
The most simplistic way to describe electronics amplifiers is your input signal is being used as a switching signal to make a more powerful circuit turn on and off such that the output is a more powerful version of the input.
Imagine if you had a morse code switch wired up to a lightning generator. Your finger presses the switch, which is a fairly small force, to complete the circuit on the lightning generator and create a much larger one. (Ignoring charging times and all that jazz, but it’s a simple visual way to describe the concept)
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