ISO Explained

ISO relates to your digital camera's sensitivity to light. The higher the number, the less light is needed to take a photo that is correctly exposed.
In bright light sunny day, you'll normally use ISO 50 or ISO 100. These are the lowest settings that can be used because of the ample light around.
However, in lower light, your camera needs some help. There are two ways of doing this:

Decrease Shutter Speed
With a slower shutter speed, the camera has more time to adjust to the amount of light it needs. Unfortunately though, the slower the shutters speed, the more chance that your images will appear blurry.

Increase ISO
Rather than decrease the shutter speed, you can increase the ISO. As stated previously, this will increase the sensitivity of the camera which means you can get the same shot with less light entering the camera. The shutter speed can now be kept low enough to avoid blurry images.
As increasing the ISO will increase the shutter speed, a high ISO will also help when taking fast moving sports shots. You'll get clear, crisp shots with no blur.
However, I still recommend you use the lowest ISO possible. Why?

Problems of using a high ISO
By using a higher ISO the camera has less light to work with. The problem with this is it also means that 'noise' is introduced into your camera. Your camera's highest one or two ISO values will produce a lot of noise (grain) in your image; it would be a good idea to avoid using the higher settings unless the light is so low that you have no other choice.

Auto ISO
Most of the time you don't need to worry about selecting the correct ISO. Most cameras have an "Auto ISO" setting. With Auto ISO, the camera will look at the amount of light in the scene and change the ISO appropriately so that the shutter speed doesn't get too slow.

ISO Values
If you choose to use a manual ISO, what values should you use?
ISO 50-100.  Suitable for bright light (e.g.: outdoors on a sunny day.
ISO 200,   Great for overcast or cloudy days. However on budget cameras some noise will be seen in your image.
ISO 400, and above.  Use for indoor or night shots, (even if you use a flash). Also useful to freeze the action in sports shots. These values will also produce the most noise.
Noise in digital cameras is a huge problem, and one we'll have to live with for a while.

But like everything in Photography Land research is continuing to be done to help alleviate this.