As you know, light can be either white or colored, in fact, most of the light we experience is something other than pure white or balanced light. We normally don't notice the different colorations of light between inside of our homes and outside in the garden, because ours eyes and brain tend to ignore it ... we know a sheet of paper is white, so we "see" it as white. It's a form of "nature's automatic white balance"!
But ours cameras lack that ability to reason and tend to see the world as it really is. On a sunny day, early morning colors tend to be "cool" (on the bluish side), midday colors are considered to be balanced, and late afternoon and evening colors will often be "warm" (on the reddish side). The reason for these color shifts during the day relates to how much of the earth's atmosphere the sun's rays must travel through to get to the ground. When the sun is low on the horizon (at either sunrise or sundown), it's rays are traveling through much more of the earth's atmosphere to reach us than they do at midday, so they tend to scatter more (off of inherent particles in the atmosphere) and that scattering causes various colorations of the sun's light because different wavelengths of light (different colors) scatter differently.
This drawing shows why the sun's rays must travel through more of the earth's atmosphere at sunup and sundown (Distance B), than at high noon (Distance A). It's roughly a 3 to 1 ratio. Okay, so we know that light (even daylight) can be something other than pure white. So what? Well, when film chemists design color film, they have to "assume" a certain color of light will be used to expose it. So they design outdoor color film for best color (most accurate color) under "high noon" daylight conditions, or roughly pure white light. So if you use film intended for outdoors to take photos inside under incandescent light (which is reddish), they'll look "warm" (orangish to reddish). On the other hand, if you were to use film designed for indoors under outside conditions (tungsten film), it would look bluish, because indoor film adds blue to compensate for the red color shift between incandescent light and daylight. Obviously we can't change the color sensitivity of the chemicals in the film, the only way to color correct it is by using correction filters on the front of the film camera's lens. But digital camera's have changed much of that.
Certainly color correction filters can be used on digital cameras (and often are in professional video (TV) equipment), but fortunately there's an even easier way to do it. Digital still cameras are in fact small, battery-operated television cameras that also happen to have the ability to capture still pictures. Don't believe it? Many still digital cameras have a video output connector on them that can be connected to the video input on a TV set or VCR. Connect it up that way and you'll see that you have a small, hand-held, real-time, color TV camera! Try it.
Since a digital still camera is basically a color television camera, the same rules that apply to adjusting a television camera also apply to our digital photographic cameras.
Without getting into the finer points of television camera engineering, a color TV camera splits the incoming light into the three primary colors of RED, GREEN and BLUE. Each of these colors, after being converted into electrical signals by the "imager", is processed separately, then matrixed together again in accordance with fixed standards, to become what is known as a "composite" video signal. This being true, coloration can be easily added to the end picture within the processing stages, and that's how "white balancing" within a digital camera is done ... coloration of the incoming light can be corrected within the processing stages of the camera itself, isn't that handy?
So how do you take advantage of that handy feature? Some digital cameras allow you select the basic processing "balance" by providing fixed "electronic filters" for the common color variations that you might run into: outdoor sunlight, outdoor cloudy, indoor artificial light, moonlight, etc. Beyond that, many of today's digital cameras will attempt to guess at what white in the picture should be, and that's called "automatic white balance" (some camera programs are even pretty good at guessing). But to get the very best color rendition that your camera is capable of, you should do a manual white balance on a white surface before shooting. Professional videographers always do. Now you might say "I've been taking digital pictures for some time and have never bothered with white balance, why do I have to worry about it now?" The answer is "you don't!" If you're happy with your photos, and you see no possibility for improvement in their colorimetry, then keep doing what you've been doing. If, however, you've had photos that you feel didn't look a good as they might have (color-wise), then this may be the answer you've been looking for. Each camera handles both automatic and manual white balance a little bit differently, so you'll have to read your camera's manual and try to decipher what it's saying, but usually you can pretty well figure it out by experimentation, once you know the basics.