When we are talking about more than a subtle adjustments the difference can be more dramatic and the image takes on a whole different mood and feel. Take the image below, taken for a Digital Photography School assignment (Simple Things: Umbrella). This was a long exposure that has a unique look as a result of the ambient light being a street light (the umbrella itself is white and green).
Now we look at the second edit below where the white balance was adjusted below 4000k (where the original was around 5700k). The yellow cast is nearly vanished, the sky a dark blue instead of black and the white in the umbrella looks white.
Just one of the ways an images over all look and feel can be altered with a single change during post processing. Each of the above files were edited from the same RAW file with Darktable.