I don't understand how black can be added in CMYK color mode. So green is made up of 85% cyan, 14% magenta, 100% yellow and 2% black. But I thought black is created by combining 100% of cyan, magenta and yellow, so where does the 2% come from?
It comes from:
1. The imperfection of inks
An ink is made from available materials, which need to be affordable, safe, reliable, etc. and they need to give reasonable results.
With the current technology, the inks are a good compromise on those points, but they are not perfect. When we combine 100% of Cyan, magenta, and yellow, they do not manage to absorb 100% of the light so the obvious choice to make things look black is to add black.
2. It is a good old friend
Let us add some additional characteristics of black ink. It is probably a good old color we are used to having on a book, since way before they were printed books, manuscripts, ever since cave paintings. It is stable, good for sharp text, etc.
3. It is cheaper in the long run
Black ink is cheaper to produce, so it is easier to use when we actually need black.
So in the current CMYK model when we need to darken a color that is first darkened with some complementary colors (1), we start adding black to the mix little by little until the dominant color on a black image is black ink. Some years ago this was a method of saving costs when reproducing color prints, trying to replace the neutralized CMY colors as soon as possible, which was called achromatic method. Now days is more important having nice vivid contrasting colors, but it is still cheaper adding black.
4. So adding the above, it is simply logic to use it
(1) Answering your second question.
Black starts to replace neutralized colors. When you have two primary colors, Cyan and Yellow; Green in your example, it has the "maximum" saturation for that color (forget for a bit the lightness of it).
When we start adding the last primary color, two main things happen, it starts to darken, and it starts to be neutralized moving it to black.
Adding black too early on light colors will be too abrupt, so neutralizing it with only the complementary is a good option (Some Magenta). When it is dark enough that this black ink does not show a clear border, we start replacing the color with Black.
Modern inkjet printers even have some light versions of Cyan and Magenta, others have lighter versions of black, so these dots and transitions are more subtle in light colors.
Let me spam you with some examples I made. The page is in Spanish but just look at the images. Here it is how a perfect CMYK ink would transition. And here is an example of how black is introduced little by little when color gets darker.
I have added this answer, although it covers what has already been said by others here, to give you a visual aid to understanding the issues.
Green doesn't need to have black or magenta in it. These have been added to darken the green.
100% CMY does not make black. It makes a dark brownish/muddy grey because as Rafael explained, the inks don't absorb all the light. Add to this the fact that CMYK inks are actually semi-transparent anyway, and you see the problem. To get a darker black you need to add black into the colour. Black ink alone does not make a dark black either. To get a "rich black" you also need to add CMY inks.
The examples below show your green in the middle of the top row. To the left is the same green without the black, and to the right the same green without the magenta and black. The bottom row left shows 100% CMY compared to a rich black in the middle, and to the right black only without any CMY inks.
Adding to the answers by others using (printing) industry terms:
While it's true that C, M, & Y can be used in varying proportions to simulate full colour in a printed image, there's a limit to the amount of ink that can be put on a page.
100% Cyan, 100% Magenta, 100% Yellow (solids) ink coverage won't dry.
That's three layers of ink on top of one another.
TAC (Total Area Coverage)
From Colour Quality Consultancy
Typical TAC values for coated stock are: sheetfed offset 300-340%; heatset web offset including SWOP (US Specifications for Web Offset Publications) 300%. uncoated stock is usually considerably less. Uncoated newsprint on non-heatset web 240-260%.
What to do?
Since this situation is a layer of black, effectively, some bright person wanted to know, "Why use three layers of expensive matched process colour inks when we could accomplish the same thing with one layer of black which is much cheaper, looks better, and dries faster?"
No one could think of a good reason so UCR was invented.
UCR (Under Colour Removal)
Whenever it's possible to substitute a black for equal amounts of process colour inks, do it.
A few jobs later, someone noticed another time and money saver.
GCR (Grey Component Replacement)
In addition, whenever a third colour is needed, black is used instead since it (in effect) adds black.
You've gotten a few answers explaining why black is used. But let me take your question literally:
Where does black come from in CMYK color mode? […] I thought black is created by combining 100% of cyan, magenta and yellow, so where does the 2% come from?
The black color in CMYK is not made by combining cyan, magenta and yellow. It's made out of carbon:
(Image from Wikipedia Commons.)
I don't understand how black can be added in CMYK color mode.
Remember that the CMYK color space is based on actual, physical ink. C means cyan ink, M means magenta ink, Y means yellow ink, and K means black ink. So, "2% black" quite literally means "put a small amount of black ink on the paper." That's how black is added.
Black pigments are cheaper than color pigments and have very good absorption across the spectrum. The CMY pigments only absorb a part of the spectrum and the overlap of the absorption curves is not perfect. For that reason, substituting black (K) for the common parts of CMY saves money and ink and improves the color representation. If one is aiming for comparatively precise colors under different illuminants, it turns out that substituting CMY with K isn't exactly equivalent, so one RGB color may be represented by more than one spot color in CMYK and not look identical under all illuminations even when the full darkness of black ink is not required.