As far as AC is concerned, the base is connected to the ground by the C3. Therefore, both input and output are connected to the base (common base amplifier). The magnitude of the current gain is less than 1 since Ic/Ie. Since it is Rc/Re, the voltage gain is high (approximately the same current flows through them) and it’s typically 250.
This circuit has a low input impedance, typically 20 ohm and has high output impedance (1Megaohm). The output signal is not inverted to the input respectively. To match low impedance devices to high impedance ones, it’s often used. It’s commonly used at VHF.