The positive power supply rail is joined to the zero volts rail 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.
Since the emitter voltage follows the base voltage, it is also called the emitter follower.
Current gain is Ie/Ib which is quite high, typically 50.
Voltage gain is only 1 because of the undecoupled emitter.
The input impedance is high, typically 500k, requiring only low power to drive it.
The output impedance is low, typically 20 ohms.
The output signal follows the input. There is no inversion.
It is often used to match high impedances to low ones. It can be used to
drive several high impedance loads.