Most appliance that use or generate a 12VDC power or signal will already have that signal isolated. In other words, if you measured the impedance from the 12V signal or its local ground to Earth ground, you would discover that it was very high - well over 1MOhms.
However, there are conditions where these 12VDC signals may not share the same ground and may be indirectly tied together though shared circuits or through grounding issues.
So, for example, if you look at the signal from source "A" by comparing the source "A" signal (Sa) with the source "A" ground (Ga) you will get the signal you expect. And the same for signals "B" (Sb,Gb) and "C" (Sc,Gc). But is you try to tie those grounds together, you could get some very high current conditions. For example, you might discover that there is a 120VAC difference between Ag and Bg.
So, by using opto-isolators, you can encode each signal into an IR level and read that IR level using circuitry with your local ground. Since there are no electrical connection between your signal monitoring circuit and circuits A, B, and C, there is no problem with possible currents among those circuits.
Let's take a specific example:
Let's say you have 16 12V batteries connected in series. What you might normally do is 16:1 MUX those sixteen signals using a common ground and then pass the result to an ADC (Analog to Digital Converter). But tying all the battery negatives together would create dead shorts across 15 of the batteries - and associated fireworks. So instead, you opto-isolate each one, and then use the MUX and ADC.