The common mode rejection ration is a measure of how well an amp can ignore noise that appears equally on both amp inputs.
If a signal and its return wire are long and have been picking up the same noise, the common mode rejection feature can be useful in removing such noise. It is important for the circuit to keep the noise common (the same) to both inputs if you want to make the best use of CMRR. For example using twisted pair wires helps keep both wires exposed/coupled to the same noise.
