To put it simply, the ISO you set on your camera affects the sensor’s sensitivity to light. ISO really relates to film, and on our digital cameras we technically have ISO equivalents. If you want all the big words and math related to it, read about film speed on Wikipedia.
ISO is an often ignored factor in achieving proper exposure. I find the following analogy helpful in understanding ISO:
Imagine a waterfall of light. (I guess you’d really call it a “lightfall”). At the bottom of the fall are buckets to collect the light. Now picture how much light you can collect in 100 buckets versus if you had 400 buckets.
Now relate that to ISO. Leaving you shutter speed and aperture consistent, you can change how much light reaches the sensor by changing how many buckets are collecting the light that is flowing through the hole (the aperture) in the amount of time the shutter is open. You’ll collect more light in that 1/100 of a second (or whatever your shutter speed is) with 1600 buckets (ISO 1600) than with 100 buckets (ISO 100).
Why would you need more buckets to collect light?
Let’s say you’re taking a picture of a person running at dusk. You’ve opened up your aperture as far as you can. Your shutter speed is 1/200 because you want to freeze motion. You need more light to achieve correct exposure, but you don’t want to change your shutter speed and you can’t open up your aperture any more. Now is the time to raise your ISO to allow your camera to be more sensitive to the light – or to have more buckets to collect the light.
Why not just always use a higher ISO?
Back in the film days, a higher ISO meant more grain in your picture. In digital images we call it noise. Once again, you can read all the technical stuff about image noise if you wish. The great thing is that as digital cameras continually become more advanced, there is less noise associated with higher ISOs. So, depending on your camera, higher ISOs will result in noisier pictures. There are several software products that you can purchase to reduce noise in your images if you have to shoot with a high ISO for some reason. And some photographers claim that noise looks cool in certain types of pictures – but that’s obviously subjective.