Color, one of the most natural elements of our daily existence, can be hard to describe. We recognize and name certain broad categories of color, like "blue" and "yellow," but it is very difficult to formalize the notion of color so that you could observe, say, a blouse of a given color and then describe it to a friend so that they would have exactly the same picture in mind.
Nonetheless, for computer graphics to work, we must be able to come up with just such a description. In fact, we must go further than that and create an encoding for colors so that we can represent them in digital form as numbers. Fortunately, it turns out that light lends itself to such an encoding. A full treatment of color, including the properties of light that it represents, the way the eye perceives it, and the range of different representations for it is not important at the moment (see the useful links below for more detailed information).
For our purposes, it will be adequate to note that most colors we need to deal with can be represented as a combination of red, green, and blue intensities. That is, we will represent a color as three values: the intensity of red light in a given color, the intensity of blue light in a given color, and the intensity of green light in a given color. We call each of these component colors channels, and we call this system of color representation the RGB color space (or just RGB).
If we devote one byte for each type of color, then we can represent 256 different levels of intensity for each component color. In this scheme, when a given value is at its maximum (255), this is the brightest, most intense amount of that color that we can represent, and when it is at its minimum (0), this is the lowest amount of that color we can have contributing to the color.
Colors that are not one of the component colors can be represented by the correct combination of the component colors. For example, we can represent purple by setting the red and blue components to high levels, and while leaving the green component low or equal to zero.
A very important thing to understand in computer graphics is that when all three color components are all equal to the same value, the resulting color is a shade of gray. Specifically, when all three components are at the maximum level (255, 255, 255), we perceive the combined color as white, and when all three components are at the minimum level (0,0,0), we perceive the combined color as black.
It is also worth noting that our choice of one byte per color channel is fairly arbitrary. Other systems of representation use fewer or more possible values per color channel. Having three color channels of 256 possible values each results in about 16.7 million colors, but in real life we perceive many, many more. For example, if we have to represent a smooth transition from black to bright red (due to shadow, let's say), we would find that having only 256 discrete colors in between the two would result in visible "bands" of color if we were really concerned about image quality. Thus, computer graphics professionals in film production often allow tens of thousands of possible values for each of the three color channels. On the opposite end of the spectrum, to allow older computers to operate more efficiently, programmers would sometimes only allow 32 possible values for each of the red, green, and blue components. Even with only a few thousand colors to choose from, surprisingly realistic images could be represented.