Why is there a capacitor in an amplifier?

Answer

Sound amplification has to do with electrical signals that you have to amplify so that a loudspeaker can move its membrane with great force. To move that membrane, you need a large voltage and large current (= power).

You can amplify those electrical signals with transistors or with integrated electronic circuits. So an electronic circuit is needed and it contains a number of capacitors.

For example, large capacitors are needed to improve the supply voltage of that circuit (smoothing the supply, making the supply more stable).

For example, small capacitors are needed to prevent the amplifier from oscillating, especially when using transistors.

For example, condensers are needed to set a number of filters. Feedback of signals, in order to improve the frequency response of the amplifier, must be done with a certain frequency filtering.

For example, capacitors are needed to separate alternating voltage and direct voltage. The alternating voltage here is the signal that must be amplified.

For example, an output filter is needed, especially with class-D amplifiers, see here.

For example, a bootstrap circuit containing an important capacitor is needed. See here.

Indeed, in an amplifier many capacitors are needed…