What is color theory? Color theory is the science of color mixing and the impact of specific color combinations. Understanding color theory requires a color wheel, which is a visual representation of how colors relate to each other. With a color wheel, you can begin to visualize the relationships between the colors of your choice, and decide how you're going to make those colors work in your space.
Say you're decorating a kitchen, for example, and your favorite color is orange. You could choose to decorate with a monochromatic scheme, which would result in furnishings done entirely in shades of orange. A monochromatic scheme may give you orange overload, though, so you turn to a color wheel for more ideas. On a color wheel, orange is opposite blue. This makes blue orange's "complementary color." Unlike colors that clash, colors that sit opposite each other on the color wheel offset each other. Choosing blue furnishings and orange accessories, for example, can really bring out the orange and make it pop. Complementary color schemes aren't the only way to introduce more than one color into your decor, though. A split complementary scheme uses three colors-- a color on one side of the color wheel, and the two colors adjacent to its complement. A double complementary scheme uses four-- two colors and each of their complements. A triad color scheme uses three colors that are equidistant from each other on the color wheel. An analogous color scheme uses two colors in the color wheel, and the shade transitioning from one to the other.
Brightness and saturation are equally as important when it comes to color theory. Saturation is the intensity of a color, from a true gray to pure color. Brightness is the lightness of a color. Saturation is the difference between a grayish lilac and a bright violet, while brightness is the difference between true red and a pale pink. Take a highly saturated purple and its split complements, green and orange. If all of those colors have different values, it can begin to clash (imagine a pastel lilac alongside neon green and dusky pumpkin). Even if you prefer to decorate with neutrals, using very saturated accent colors are a great way to accentuate strong black or white decor.