In addition to being an element of design, color is also whole entire body of theory called, not surprisingly, color theory. Color theory is concerned primarily with the properties of differing wavelengths of light and how we perceive them. But it's also focused on the interaction of colors, i.e. how different combinations of colors can cause colors to change in the appearance of the consituent colors.
In the world of color theory there are actually competing sub-theories or approaches to how we relate colors. These theories go back centuries, but lets arbitrarily start with the work of Bauhaus artist and educator Johannes Itten and his 1961 piece entitled Farbkreis, a German word that translates literally to "color circle."
Johannes Itten, "Farbkreis," 1961
This piece reflects a more painterly understanding of colors — unsurprising, as Itten was himself a painter (in addition to a weaver). The classic primaries red, yellow, and blue are considered so because they cannot be made by mixing other pigment colors.

For painters and other types of artists and designers who manually mix pigments, Itten's system works well. But contemporary color theory is really more concerned with frequency interaction between differing hues, and how to represent colors accurately with different types of technology. These technologies fall into two distinct categories - screen-based and print-based - and the various colors systems used in each couldn't be more different.

Contemporary color wheel; Color systems; Color types
GDPE diagrams color systems 33Additive color systems arise from the direct mixture of different wavelengths (colors) of light. The primary colors in an additive system are generally red, green, and blue. Laptops, desktops, smartphones, tablets, televisions, portable gaming systems, smart watches...basically anything with a color screen combine, or add, red, green, and blue-colored light in various combinations to generate about 90% of the colors you and I can see. Combining all of these primaries in equal parts will generate white light. A system like this is specifically called an RGB system (see below). Therefore, any design work meant to be viewed on a device of some kind - e.g. broadcast graphics, video, app assets, web site imagery, etc - should be created in an RGB system or mode.

GDPE diagrams color systems 32Subtractive color systems arise from the filtering of light. The most common primary colors used in a system like this are cyan, magenta, and yellow. Generally you will find this color system in the four color printing process, where a black 'channel' or 'key' is used to register or align the other three colors together. As the alignment key, black is generally shorted to K, and the entire system labeled CMYK.

In the case of CMYK, the pigments placed upon (usually) white paper act as filters, absorbing or subtracting wavelengths of light other than those corresponding to the colors we perceive. This is why systems such as these are called subtractive: light is filtered or subtracted when colors are generated. 

Anything kind of digital work that is meant for print should be made in the CMYK space. 

Color Schemes

There is no right or wrong way to mix colors, as acculturation and personal preferences play a large role in what we find acceptable. However, basic color schemes that use the modern color wheel can be very useful in discovering universally acceptable color combinations. Below are the six geometrically derived color schemes, and respective examples of palettes obtained from them: 

Color schemes derived from the color wheel