Why does input buffering improve differential amplifier performance?
Take a look at the basic schematic of a diff amp created from a single opamp.  You will notice that the two inputs aren't high impedance, and that one of them is also coupled to the other.  By adding buffers in front of each of these inputs, the inputs of the combined diff amp become high impedance and not coupled to each other.

The designer of this 3-opamp diff amp (often called a instrumentation amp) can trade off where gain is applied.  The main diff amp can be configured to provide the gain, or each of the buffer amps can also have gain.  Usually the buffer amps have unity gain because anything else can't be done as accurately.  Any mismatch in the gain of the buffer amps reduces common mode rejection.