C10 is a decoupling capacitor, but why so big? The amplifier draws a lot of power suddenly, and if the power supply can't keep up with the sudden demand in spike, there will be audible distortion. By adding a very large capacitor, the amplifier is free to draw as much power as it needs to handle it, resulting in a smoother listening experience.

C12 is there to remove the DC component from the audio signal. This ensure that the speaker can make the most of its dynamic range.

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