In traditional (film) photography ISO was the indication of how sensitive a film was to light. It was measured in numbers (you’ve probably seen them on films - 100, 200, 400, 800 etc). The lower the number the lower the sensitivity of the film and the finer the grain in the shots you’re taking.

In Digital Photography ISO measures the sensitivity of the image sensor. The same principles apply as in film photography - the lower the number the less sensitive your camera is to light and the finer the grain. Higher ISO settings are generally used in darker situations to get faster shutter speeds (for example an indoor sports event when you want to freeze the action in lower light) - however the cost is noisier shots.

Below are two enlargements of shots - the one on the left is taken at 100 ISO and the one of the right at 3200 ISO.