Sometimes you need a certain shutter speed to get the shot you want; maybe an action shot at a sports event when you don't want to have movement blur, and there just isn't sufficient light get it. Alternatively you may be taking a landscape shot with slow shutter speed but the narrow aperture means there isn't enough light getting through. One answer to this is to increase the sensitivity of the sensor, or 'increase the ISO.' With film the ISO was the sensitivity rating of the film itself; the higher the rating the more sensitive was the film. With digital photography the same thing applies only it is now the sensor that becomes increasingly sensitive to light as the ISO setting increases. This means that at a higher ISO setting less light needs to reach the sensor to create the image than would be required on a lower sensitivity setting. There is a trade off for this though and that is a lower quality image. With film we get grain, with digital we get noise. Ideally we try and keep the ISO setting as low as possible to get the best quality we can, but as mentioned above, this isn't always possible. Sometimes it's better to get the shot with a bit of noise than to have nothing at all.
In the exercise we are asked to provide examples of this by taking one photograph which didn't quite work at a low ISO (for example the image was blurred due to a low shutter speed being required, or the depth of field was too shallow due to a wide aperture) and then another where a higher ISO had allowed the problem to be resolved. To be honest, I found it difficult to find examples easily, so most of the shots aren't particularly interesting. However, I have satisfied myself knowing that I understand the scenarios when changing the ISO setting would be beneficial.
I found this exercise quite difficult to work on as I was continually attempting to concoct situations where increasing the ISO allowed me to create a better image, whereas all I ended up doing was increasing the shutter speed or decreasing the aperture until the image was too dark and then raising the ISO so that it was brighter again. This clearly isn't the purpose of the exercise! I do understand that ISO is the '3rd way' to increase the exposure of an image, and allows you more flexibility to select the aperture and shutter speed you would like, although at the expense of digital noise.