ISO is the measure of a Camera's digital sensor's sensitivity to light just like the film speed in the old days. A high ISO means that it takes less light to make an exposure than a low ISO. As a general rule the lower the ISO the higher the image quality and vice versa. When the ISO is increased the noise (or grain if using film) increases degrading the image. The following is a quick list of the ISOs that most DSLRs have: 100, 200, 400, 800, 1600.
The images below represent two different ISOs to give you an idea of the image quality you might see at different ISOs.
So, why do you pick one ISO over another? Well, it depends on the light situation and what kind of shutter speed or aperture you want and what type of image quality you can live with... Personally, even with noise reduction software I find it difficult to live with an ISO above 400. Newer full frame cameras have incredible ISO performance so technology is changing the way we shoot. Still you should always choose the lowest ISO you can get by with for greater image quality. For more information on exposure check out my previous blog posts on Shutter Speed and Aperture.