According to the fact that the camera acquisition sensors do not match the sensors in the human eye, the white balance setting is necessary.
In order to capture an image, of course, we need some light on the subjects. There are many sources of light such as the Sun, light bulbs, or a flash light from camera itself. Different lights have different color tone. For example, some source like fluorescent light has more green colors than another. A camera image sensor is able to see the differences, but human eyes have hard time to determine the colors from light. Normally, we see just a white color from most of light sources.
If you want to take a shot under, let say, the Tungsten bulb, you may have to adjust the white balance to Tungsten. Otherwise, the color tone of your image might look strange. Let see the difference between the following two pictures.
The first picture on the left is captured with Day Light white balance. In contrast, we set the white balance to Tungsten for the second shot, and we got the picture on the right. The explanation is a Tungsten bulb produces more yellow colors then the day light which is white by nature. However, our eyes couldn't see much difference, but cameras do. Thus, cameras need color adjustments so they can capture images as if the color from the light source is white. In our case, since there is more of yellow color from a tungsten bulb, by setting the white balance to Tungsten, we put some blue color to make the light source white. That's why it's called White Balance.
Usually, it's a good idea to set the white balance according to the light source, but there are some exceptions. One of them is when you intentionally want your image to look strange. In other words, we can treat the white balance setting as a color filter. Suppose you desire your image to look more yellow. You can use the Tungsten white balance. Or, you can have magenta color filter with the Fluorescent white balance.
Technically, we measure the difference between light sources with the color temperature under Kelvin scale. Color temperature is based upon the principle that a black body radiator emits light whose color depends on the temperature of the radiator. For example, the day light situation has about 5,000 degree Kelvin. A tungsten bulb has about 1,500 degree Kelvin.
(pictures source: go_med @ rpst-digital.org)
ISO, Aperture, and Light Condition part 1/2
ISO, Aperture, and Light Condition part 2/2
More on Shooting Tips