In the Common Drain Amplifier configuration, the drain terminal is at AC ground.
The input is applied between the gate and drain terminals, while the output is measured between the source and drain terminal.
Since the drain terminal is common between the input and output side, it is known as Common Drain Amplifier.
The Common Drain Amplifier has
1) High Input Impedance
2) Low Output Impedance
3) Sub-unity voltage gain
Since the output at the source terminal is following the input signal, it is also known as Source Follower.
Because of its low output impedance, it is used as a buffer for driving the low output impedance load.
Often in multistage amplifiers, while driving low impedance load, the source follower is used as an output stage.
Fig. Common Drain Amplifier (Source Follower) with Biasing Circuit
In the given PDF link, through a small-signal analysis, the expression of input impedance, the output impedance, and the voltage gain of this common drain amplifier is derived.