Primary colors are the fundamental hues that can be mixed to obtain all possible colors and cannot themselves be created by combinations of other hues. There are different primary colors for the additive and subtractive systems and an additional set of three traditional artists' colors.
The subtractive primary colors are cyan, magenta and yellow. These are the primaries used for color printing, all three together in equal amounts make black. It is a subtractive system because the color perceived is the light reflected from an object that absorbs energy at the other wavelengths that make up visible light.
The additive primary colors are red, green and blue, those recognized by cones in the human eye. Red, green and blue light combined in different amounts form other colors. All three together in equal amounts make white light. It is an additive system because the color perceived is a specific combination of the primary colors. This is how a video display shows color.
The traditional artists' primaries of red, yellow and blue are not technically primary colors. No combination of them can create all the hues of visible light although they can be combined to form a wide range of colors.
No model can completely describe the full range of colors we can see, but some are better than others. Color mixing in practice is not perfect, particularly with pigments. Black is routinely included as a fourth "primary color" in printing color images and many different substances have been used as pigments in an attempt to match particular colors.
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I wasn't sure how well this would go over. Specifically, I thought the discussion of different sets of primary colors could be a problem if someone was expecting to see only "red, yellow and blue" and didn't care to know the technical details of things like additive and subtractive. I didn't go out of my way to make this technical, but was certain that what I said was clearly based on physics and physiology. As a technical person, this is an important part of how I understand color.