White balance reveals an interesting difference between a camera and a human eye: A human eye has a human brain attached. When you look at a white object, your brain is actually interpreting the lighting cues around you and calculating that the object is white on the fly. If the object is under a blue light, it will really look blue, but your brain compensates for the color difference, so you'll see it as white. The camera does no such compensating unless you force it to do so, so if a white object is under a bluish light, the camera will record bluish pixels.
Adjusting white balance helps force the camera to compensate for the fact that most lighting conditions aren't perfectly white. Many indoor lights have a yellowish tinge to them, while fluorescent lights have a bluish tint. Even natural light is a little bluer than you might think. You can set white balance manually by adjusting it up or down or selecting the appropriate setting, then taking some test shots to see which ones look most natural.
Alternately, you can use a camera's automatic white balance function. Just aim the camera at a white object, such as a large sheet of paper (this is why news vans are almost always white -- so the camera operator has an easy way to set white balance). When you hit the white balance button, the camera will automatically adjust to the lightning conditions.