Common-mode operation is application of same input signal at both the input terminals. Since the two inputs are equally amplified, they appear with opposite polarity at the output and the resulting output is zero. This is the ideal case. But in practice a small output signal is present.
The best characteristic of common-mode operation is that the difference is highly amplified and the common-mode signal is reduced in size. Thus, the operational amplifier amplifies the differential signal and rejects the common-mode signal.