Color theory is the study of color and its role in art and design. Obviously, humans have been thinking about colors for thousands of years, but modern color theory really arose in the 1800s, when it began to diverge from science into a pure art. A knowledge of this theory does require some understanding of basic scientific principles about color and perception, but much of modern color theory surrounds the way that people view, think about, and interact with colors, from those used on their walls to the hues in a company logo. This field incorporates psychology, history, and criticism just as much as it does science.
The field of color theory is quite large, with a number of prominent theorists and authors who offer commentary on the issue. It could be said to be about a lot of things, but fundamentally it is an examination of color, how color is formed, how colors are arranged, and how they interact. Color theorists look at how the context of a color changes it, for example, or how various colors work for or against each other in compositions ranging from paintings to brochures.
Many people can look at something and confidently say that the colors clash, but they cannot explain why. Someone who has studied color theory can look at the same object and discuss how the saturation of the colors, their tones, their placement, and their context combine to make them clash. “Clashing” colors aren't necessarily bad things, but a lack of color harmony can be quite unsettling, as you may have noted if you've ever tried to pair, say, red shoes and a red sweater; small variations between the reds can completely ruin the look.
One aspect of color theory involves the study of the historic use of color. Color theorists look at the shades which dominated particular eras in art, for example, for clues to the societies that the art was produced in. Some artists theorize, for example, that the dark, subdued tones which dominated Northern European art for much of the Middle Ages were related to the “little ice age” of the era, which made European life significantly darker and more dull. Colors have also been important historically because some were quite expensive and difficult to obtain, due to the ingredients needed.
Students of color theory also like to look at the meanings of specific colors, exploring the use of things like bold colors in company logos, or the subtle messages which people might be sending with something like sage-green stationery, for example. These color theorists also look at the ways in which colors change a space, making recommendations for interior design based on the space and how it will be used.