White Balance is a function on digital cameras that allows you to influence the color balance of your images. The point is to make colors in your picture look like they do in real life. It's called white balance because it can help make your whites look white, but it really affects the hue of all the colors.
The reason White Balance is important is that different light sources (incandescent light bulbs, fluorescent light bulbs, the sun . . .) produce different colors of light. Our eyes are used to these differences and our brains make adjustments so we can still tell something is white when it has orange light on it. The problem is that when we take a picture under one kind of light and then look at it outside of its context, the colors will look wrong.
If you've never adjusted the white balance (WB) on your camera, it is probably set to auto. In auto mode, your camera will do a fine job guessing at what kind of light is illuminating your scene most of the time, but sometimes it needs help. If you notice that the colors in your picture are "off" you can help your camera by telling it what kind of light there is.
Here are examples of what WB can do. Notice how the colors are different in each image. FYI, the cloudy setting produced the most accurate colors . . . and it was cloudy when I took the picture.