CMYK, Cyan Magenta Yellow blacK, is the 4-color color space used by most printing processes, particularly offset printing.
See the article on color to compare this format with others. There are basically two kinds of color models available. One is called additive and it the method used to display colors on the screens used on electronic devices. The second is called subtractive and is the colors that you see in paintings, photos, and the rest of the objects you see every day. Objects show color when they are lit up from a light source like the sun that nominally has all of the colors mixed, a white color. The color system is called subtractive due to the fact that the object you see in a particular color is reflecting that color while absorbing all of the other colors. The dominant subtractive color system in use is CMYK although several others exist. When I was growing up and started learning to paint in school we used red, blue, and yellow as our primary colors but then we had additional colors available in the palette without having to mix them. When we did mix them we could use more of less of one color with respect to the other to get the color we wanted. We could also mix in white paint when needed. Painters throughout history have sometimes been limited by the available color pigments that could use.
 Inkjet printers
CMYK is also the color space used by the marking engine (that part that actually marks the paper) in common inkjet printer although their firmware and drivers are designed to translate RGB (Red Green Blue) color space images on the fly. The printer contains 4 cartridges containing the 4 colors and can print over the same area to make additional colors. As shown in the image above mixing of the three main colors can produce an additional 3 colors, Red, Blue, Green, and a form of gray, all at full intensity. The fourth cartridge is Black, also called the Key color and it used to produce black when needed. Some believe the K in CMYK means Key color and others insist it is Black with K being use to avoid confusion with B as a reference to Blue. In any event the Key color is most often Black. The term Key is used to identify the edge of the image for alignment purposes which is usually accomplished with a black line.
In order to product more that 7 colors you would to be able to add levels of white to lighten the colors. Since the printer can only produce full colors it depends on the paper itself to add the white value. This is done using a process known as halftone. The idea is that if you want a lighter color then print the main color with many dots separated on the page allowing the white to show through. The wider that separation the lighter the color will appear. In practice this is done with a rectangular dotted pattern on the paper with varying width pattern as needed. To avoid moire effects the various colors arrange their rectangular dotted pattern in different angles with respect to the edge of the paper. If the dots are small enough and close enough together the person looking at the page will just see the overall color effect. Similarly gray patterns can be generated using the single black cartridge. This is related to grayscale dithering.
 6 color
The darker colors of magenta and cyan need more separation to lighten their color than the already bright yellow. This additional separation can sometimes show up to the user as a fainter color. To avoid this some printer companies have developed a 6 cartridge color system with lighter color cartridges for magenta and cyan. This is referred to as a CcMmYK color system with small letters representing the light colored cartridges. Sometimes this may be called CMYKcm.
Black is also a dark color and a seventh color, gray, could be used in a similar way but the combination of the three colors already produce a gray color which can be utilized to avoid the need of a seventh cartridge.
 Other printing
The same approach is used for most printing machines. Newspapers and some other book printers can only print one color at a time. They produce color images by printing the same page several times with different color inks used each time. Similar different color plates can be used to superimpose on each other to produce multiple colors out of the main primary colors. This approach with separate plates is called offset printing.
 Digital Color
Color pictures in CMYK can be stored in a digital file to be used directly for printing. Generally CMYK thinks of color values of the range 0 to 100. But for digital files the value are often expanded to use full byte storage. One hundred values is deemed adequate to define each primary color and black.
Digital Formats that support CMYK include PDF, TIF, JXR, PSD, and BPG. Many graphics programs can also support CMYK and can often convert images from one form to another, such as to RGB. It can be problematic to get exactly the same colors through this conversion. An ICC Profile can aid it getting the colors right.