In short, ISO is the sensitivity of the film or digital sensor.
To give you the best example of what changes in ISO does to a photo, I made a chart below. Using a ribbon origami rose that I made, these photos are taken with a Canon 40D, so different cameras will have different results. The large picture at the top is taken at the lowest ISO of 100 to show what the entire picture is. Below that I have images of each ISO setting at 1/3rd increments. These are 100% of the pixel size right out of the camera. For each ISO change I had to also change the shutter speed. The aperture was the same in each at f/5.6.
At the beginning I have the two extremes of the highest and the lowest next to each other to show the dramatic difference. Then at the very bottom that full photo is taken with 1600 ISO. The reason I did this is to show, depending on the use (here being the web), a high ISO will still be a suitable option. At this small size on a website, the noise is barely noticeable. But blow it up to a 16×20 print and the difference between them will be quite intense. I very rarely would use 3200 ISO, and isn’t really native to this camera (thus the H). But it is nice to have available in a pinch.
So what is it all about then?
ISO is a standardization that was