Well the answer is actually quite simple.
If you painted something on a piece of paper, then that is what you show somebody, it’s that way, and it’s stuck that way. People may see it differently because of the characteristics of their eyes, or because they have some level of colour blindness or because they are seeing it in different lighting, but essentially, what you present to them is THE item, The Colour as you intended.
So where does colour calibrating your monitor come in? We know that monitors generally found on people’s desks are only 8-bit RGB monitors, and shows limited ranges of colour, we know that now everybody calibrates their monitors, but that is something that is outside of our control. We need to work for the majority that does do it. And we need to adjust our colour at least for the central or primary object in our image or footage.
If your computer monitor is not calibrated, and you match your colour “by Eye” to an object next to you, you will most certainly mismatch the true image, and the image received on the other side by your client on their calibrated monitor will be off by quite a bit! The lighting in your studio or retouching area may be cool, or hot in colour, you might be wearing a brightly colored shirt today reflecting off the subject you are matching to, etc, etc… there are tons of reasons why you will be unable to match the colours accurately, except by pure luck.
Oddly enough, having a degree of colorblindness may actually help you to match better (I used to work with a colorblind printer that could read negatives like nobody else, simply because she sees tones, not colours, and adjusted her printing in relation to the tonalities and depth of the tones) but think about it for a second… all things being neutral, If I have to match a red block on my shooting table to a red block on my screen, I can more or less do it, even if I am off by a few points, because I will perceive the colour in the block, the same way I perceive the colour on the screen.
BUT… If your computer thinks you are looking at orange, but your screen is showing you red, then the client will get a completely mismatched images on their side with a calibrated monitor/screen setup. You can try and match “by Eye” using things like Adobe Gama, but your result will be questionable at best (food and medication has a definite implication on your sight) if you are tired, you may see more contrasty, while other see colours more dull. Taken some item like Viagra… many patients reports a blue cast to the world, some medications cause a green cast, yet others orange. The best way to take the guesswork out of the equation is to calibrate using a tool like a Colormunki or Spyder colorimeter. Something not influenced by day to day events in your life and diet and that takes your surroundings and lighting into account.
Except for more accurate colour, you also get the added bonus of more consistent output. As a stock photographer, I have a bit of leeway on matching skintones or the colours that I put out, but a wedding shooter is a different story! 2 years down the line, the mother in law will come in and say she wants two enlargements for the two grandmothers, exactly like the one hanging in her dining room. In the print days, we would just print 3 and destroy the original, because matching them up was close to impossible (too many variables, differences in paper, temperature of chemicals, etc, etc) but today, it’s actually quite possible to give good, consistent results if your colour profiles are up to date, and you have a calibrated system to start out on.
Below is an excellent example. This is an image edited by an “editor” employed by me at some point, working on a supposedly “calibrated” screen and system, however, it’s clear to see that the skin tones are un-naturally red. But how do I know that’s not what the model looked like? because the white-point is about 16points off on the RGB scale any “true grey” would have very close to even RGB values (i.e. 230.230.230 or similar this is 238.226.210 you can have a slight discrimination in ha values, but that is too far)
Also, matching a skin tone to the X-rite Caucasian colour chart (top block) reveals too much red in the actual skintone (second block, average random sample)
By the way, if the skintone on the model’s face seems normal to you, then you need to get yourself to the photographic shop and buy a colorimeter or to a doctor to adjust your prescription!