Common-mode rejection ratio, CMRR, is defined as the ratio of the differential voltage amplification to the common-mode voltage amplification, ADIF/ACOM. Ideally this ratio would be infinite with common mode voltages being totally rejected.
The common-mode input voltage affects the bias point of the input differential pair. Because of the inherent mismatches in the input circuitry, changing the bias point changes the offset voltage, which, in turn, changes the output voltage. The real mechanism at work is ΔVOS/ΔVCOM.
In a Texas Instrument data sheet, CMRR = ΔVCOM/ΔVOS (gives a positive number in dB).
CMRR, as published in the data sheet, is a DC parameter. CMRR, when graphed vs. frequency, falls off as the frequency increases.
A common source of common-mode interference voltage is 50 Hz or 60 Hz noise from the AC mains. Care must be used to ensure that the CMRR of the op amp is not degraded by other circuit components.