It is a powerful idea to explain the abstract electronics circuits by simple electric concepts. Thus, the common-mode operation of the 4-resistor op-amp differential amplifier can be easily explained by the basic electric circuits of voltage divider and balanced bridge.
Equivalent electric circuits
1. Voltage divider. The pairs of resistors R1-R2 and R3-R4 form two identical voltage dividers. Both are grounded (the first - by the virtual ground at the op-amp output; the second - by the real ground) and their inputs are driven by the same input voltage source.
2. Balanced bridge. Actually, the two voltage dividers form a balanced Wheatstone bridge with varying supply. Its unique property is that the voltage drops across the opposite resistances (R1<->R4 and R2<->R3) are equal; so the difference between them is zero.
1. VIN = 0. Initially, the input voltage is zero. So the op-amp output voltage is zero and the R1-R2 voltage divider is virtually grounded.
2. VIN = var. When the circuit input voltage changes (common-mode), both op-amp input voltages simultaneously change with the same rate so that their difference is always zero. The op-amp output voltage does not change since it depends only on the difference between the input voltages... and this difference is zero. So the R1-R2 voltage divider remains virtually grounded.