What is the purpose of a coupling capacitor?

Answer 1

A coupling capacitor does the same work as its name suggests, that is coupling one stage of the electronic circuit with another. It does that without passing the DC bias voltages between stages so that these stages are not affected by each other.
To block or avoid the flow of D.C and to allow only A.C

Answer 2

if we want to stop the dc voltage and pass the ac signal we must use coupling capacitor in an amplifier....