Artists can use colors for many reasons besides naturalism (representation that looks like the real world), including setting moods and highlighting importance. The colors of the world can be divided on a few scales. When we use the term “color” casually, what we usually mean is hue. The hues appear on the visual spectrum:

On the spectrum, we see the pure hues. These can be divided into Primary, Secondary and Tertiary colors. Primary colors are (for most art media) red, yellow and blue. All the rest of the colors can be made from these. Secondary colors are made by mixing two primary colors: Red and yellow make orange, and so on. Tertiary colors are made by mixing a a primary color with a secondary color:

The colors on the left of this wheel are called cool colors and those to the right are warm colors. Using warm or cool colors in an image can create moods. Pablo Picasso used cool colors for his The Old Guitarist, creating a cold, harsh scene. Henri Matisse used warm colors in his The Joy of Life, creating a warm, sensual, inviting scene.
Value is the degree of lightness or darkness of a color. If we add white to a hue, we get a tint. If we add black, we get a shade. Tints tend to be more cheerful and lighthearted in feel. There are many tints in The Joy of Life above, and many shades in The Old Guitarist.

Finally, saturation is how bright or dull a color is. Matisse tended to use very saturated colors, as in his The Dessert: Harmony in Red, whereas in this self-portrait, Rembrandt van Rijn relied on a much more muted palette with very little saturation of colors.

 Contrast is the amount of variation between the highest and lowest values in a work. This is perhaps most commonly used to talk about photography, but can be applied to any works. The 1903 Alfred Stieglitz photo of the famous Flatiron Building in (my native) New York on the left has low contrast, whereas the 1985 Robert Mappelthorpe photo on the right has much higher contrast, meaning that the difference in the whites and blacks is much greater.