Raising your ISO is a great way to handle low light situations. In darker areas, you generally need longer shutter speeds to allow enough light to fall on the sensor. If you increase your ISO, though, the sensor will record light faster, and you can maintain faster shutter speeds. This can help you keep your images nice and sharp even in low light. The downside to raising your ISO is that your images will become more "noisy." In photographs, a noisy image will appear grainy, so you want to use the lowest ISO that will give you the shutter speed you need.
Digital SLRs today often allow you to get great results at high ISOs. Generally speaking, the larger your camera's sensor, the better it will be able to handle shooting at high ISOs. Most point and shoot cameras have small sensors. On mine, I try to shoot mostly in the 80-200 range, going up to 400 only if I need to. Most consumer grade SLRs have larger APS-C size sensors, and many new ones can handle ISOs of 1600 without much difficulty. Many professional grade SLRs have even larger "full frame" sensors that can shoot up to 6400 ISO or higher with manageable grain.
The above image was shot with a Canon EOS 40D (APS-C size sensor) at 1600 ISO. I wanted shutter speeds around 1/100 sec ensure I got sharp pictures of the performer, and that ISO allowed me to do that.