Why do we calculate input/output resistance?

Input and output resistance calculations for amplification purposes plays into the input and output impedance of the circuit.

The input and output impedance gives information on the bandwidth on both input and output of the circuit (i.e. how fast capacitances can be charged and discharged) as well as the impedance needed to drive the circuit and the impedance that the circuit can drive.

You know voltage dividers right? Well, when you hook up a voltage signal driver up to a signal receiver, the driver's output impedance forms a divider with the receiver's input impedance. If the driver's output impedance is significant relative to the receiver's input impedance, then most of your voltage signal will be lost across the driver's output impedance and never make it to the the receiver. You've heard of this concept, right? So, if you are using voltage as your signal that carries information (as opposed to current), you want your driver to have a low output impedance and the receiver to have a high input impedance relative to each other.