When we talked about impedance matching, we talked about input and output impedance as the impedance viewed from different parts of the circuit. Can you explain that again?

The input and output impedances we are discussing in the context of transistor amplifiers are in fact exactly the same as what we were discussing before. The input impedance is the impedance ``seen'' from the input. Imagine the circuit as a black box with the input terminals poking out from it, put a voltage $V_{\rm in}$ across the terminals, and measure the current $I_{\rm in}$. You would infer that the black box has an impedance $V_{\rm in}/I_{\rm in}$: that's $Z_{\rm in}$, the input impedance. Similarly, imagine ``looking'' at the black box from the two output terminals: the ``Thevenin equivalent'' impedance is the open-terminal voltage over the short-circuit-terminal current, i.e., $Z_{\rm out} = \frac{V_{\rm out}(R_L=\infty)}{I_{\rm out}(R_L=0)}$.

Now for impedance matching: that's the idea that when you have power supply impedance and load impedance the same, you get maximum power transfer (worked out in Eggleston 2.9 in the context of transformers). In this context, the power supply Thevenin equivalent resistance is the output impedance of the supply, and the load resistance is the input impedance of the circuit you attach to the supply. The concept actually holds generally for input and output impedances of four-terminal networks you attach to each other- when the input impedance of the second is matched to the output impedance of the first, power transfer is maximum. This is a reason you often want to know input and output impedances. (Also, matched impedances suppress signal reflections, although we haven't really talked much about that.)

...So for the RLC circuit is $Z_{\rm in}=Z_{\rm out}$?

Well, if you work out input and output impedance for a passive RLC network, you will find that in general $Z_{in} \ne Z_{\rm out}$. $Z_{in}$ will be $R+\frac{1}{j\omega C}+j\omega L$ and $Z_{\rm out}$ will depend on where you are taking the output.

But indeed, for the RLC circuit also, power transfer from the supply is maximum when the input impedance of the RLC circuit (which depends on $\omega$) is matched to the output impedance of the power supply at the input of the RLC circuit.