Common-collector amplifier is also called emitter follower as emitter voltage follows the base voltage. In common-collector circuit, the output is taken in the emitter lead instead of the collector.

As shown in the circuit diagram, the positive power supply is connected to ground by C3. As far as AC is concerned, both rails are joined together.

Therefore they, and the collector, are common to both input and output.
Current gain (Ai=Ie/Ib) is high.
Voltage gain (Av=Ve/Vb) is only 1 because of the undecoupled emitter. The input impedance is high(approx. 500K) while the output impedance is low, (approx. 20 ohms) requiring only low power to drive it.The output signal follows the input and there is no inversion.