What exactly is ISO? Well since it's stands for International Organization for Standardization, I think I need to explain no further. But for those of you who want to know more, I suppose I can continue...
In short, ISO is how sensitive your camera's image sensor is to light. The lower the ISO, the less sensitive and vice versa. The Image sensor is responsible for converting light into an image. As you can see, it's a little bit important.
In low light situation were you either don't want to use a flash or just don't have one, you can make your camera's sensor more sensitive to light by increasing the ISO. While this will help you capture a properly exposed image, it does end up adding some noise to your photo. In an ideal world we would all take pictures at our camera's lowest (Base) ISO. This would produce the highest quality image without adding noise to the picture.
Each increment up from your camera's set ISO doubles the sensitivity of the sensor which is why the ISO doubles in value with every increment.
This brings up an important question: Why would you increase the ISO if the lower it's set, the better? Sometimes if you want to freeze motion in low light without a flash, the shutter speed can't be set fast enough regardless of your aperture. Raising the ISO to a higher increment will allow you to make the shutter speed faster. While your image will have more noise, today's software (Lightroom, Capture One, etc.) can reduce it fairly well.
Now get to shooting!