A rotary encoder is read by a microcontroller which i turn controls the amplifier circuit to set the desired volume. Another way to control volume is with simple up and down buttons. They are probably connected to a microcontroller as well which controls an amplifier circuit.
As the name suggests, the purpose of an amplifier or an op-amp is to amplify or increase the input signal to produce an output signal which is much larger than that of the input, with a similar waveform as that of the input. The main change in the output signal will be the increase in the power level.
Ceiling speakers are a long-term audio solution and will provide you with room-filling sound for decades to come. That’s why it’s so important your speaker choice is carefully aligned to how much sound quality you want to get from your speaker in that specific room.