Imagine you have a 1 volt difference between two inputs that you wish to measure.
Ground the most negative input. The more positive input is at 1 Volt.
You connect a differential amplifier with a gain of 1 (in this example) to the two inputs and it provides a 1 volt output.
Now, leave the amplifier connected but disconnect ground from the negative input so the inputs are floating but 1 Volt apart.
Now stand on a convenient high voltage insulator that just happens to be around and eg stand in the path of a beam of positive ions that happens to be passing by - so that your potential relative to ground increases continually.
Input voltage on two inputs
Difference --> Result
2-1 = 1
12 - 11 = 1
102 - 101 = 1 --> 100 Volt common mode. Magic smoke
1002 - 1001 = 1 --> 1000 volt common mode. Bright flash
1,000,002 - 1,000,001 = 1 --> 1 million volts common mode. Br......
In all cases the differential voltage is 1V.
But the increasing voltage on the inputs after a while gets to voltages that cause interesting results.
NB - this is a genuine real world problem that needs to be addressed. "Static electricity" can easily produce thousands of volts on a floating input.