ISO is a term carried over from analog photography and refers to the sensitivity of the film. The lower the ISO, the lower the sensitivity of the film and the more light (aperture +shutter speed) you need to properly expose the photograph.
The ISO also dictates the quality of the image. For analog photography, films with a high ISO have more grain in the image. In digital photography, image degradation is seen as noise. Low ISO images not only have a much finer grain, but also tend to provide richer colors in the final image.
Because low ISO settings need more light - longer exposure times or higher apertures (leading to shallower depth of field) - photographers have to carefully balance the quality of the final image over the speed at which the shot must be captured. Where the subjects are fast moving (sports photography, children, and animals being prime culprits here) the need for a fast shutter speed to capture anything close to an in-focus picture may override the desire for a low ISO. Thankfully, digital technology has improved the image quality at higher ISOs and good digital cameras can capture passable quality images up to ISO 1600.