In the most basic of terms, ISO is the level of sensitivity of your camera to available light. The lower the ISO number, the less sensitive it is to the light, while a higher ISO number increases the sensitivity of your camera. If you remember back in the days of film, we use to buy film with a ASA rating, such as ASA 100, ASA 400, etc. This expressed the films sensitivity to light, or commonly referred to as the speed of the film. Today's camera do not use film, but use image sensors instead. ISO is basically a ASA equivalent. The ISO setting denotes how sensitive the image sensor is to the amount of light present. The higher the ISO, the more sensitive the image sensor and therefore the possibility to take pictures in low-light situations.
Back in the days of film, you had to physically change the film if you wanted a different ISO, but with todays digital cameras, you can simply set the camera to whatever ISO speed you want. Pretty nice huh... just one of the advantages of the digital world.
Having the ability to change your ISO on the fly helps you always get the shot. Suppose your in a low light situation, and your camera can't obtain a correct exposure, you could use a flash, but what if your in a museum, or concert where flash photography is not permitted. All you need to do is use a higher ISO setting, this will allow you to obtain a correctly exposed picture.
Another example is, if you find your camera is selecting a shutter speed that is too slow (1/60 sec. and slower) to handhold and thus resulting in blurry pictures. Selecting a higher ISO will then allow you to then select a faster shutter speed so you can get your shot.
Oh course there's always a price to pay for versatility. Increasing our camera's ISO setting can introduce what is called digital noise. This is a necessary evil, the higher the ISO the more noise. But I wouldn't worry too much, about digital noise, as todays cameras have greatly improved picture quality at higher ISO speeds. Just remember to shoot at the lowest possible ISO setting for the lowest noise and best dynamic range.
So, get out your cameras owner manual, and read up on how to adjust/set your cameras ISO settings. Having this knowledge means you'll always be able to get the shot in low light..