There will be times, when you simply cannot slow your shutter speed enough; you have opened the aperture of the lens as wide as it can go, and you just don’t have enough light to get a good enough exposure.
When such a situation arises, it is time to adjust your ISO
The topic of ISO was very briefly touched upon in the Water In A Bucket article, and as stated the ISO was essentially the size of the bucket.
A smaller bucket is easier to fill, and therefore gives greater flexibility when setting your shutter speed and aperture in a greater number of lighting situations.
The depth of field issues you may encounter as you adjust the aperture; the motion blur you may capture as you adjust your shutter speed; ISO too has a possible outcome in your final image: Grain.
Adjusting the ISO too sensitive (The higher the number i.e. ISO 6400) will create unwanted specks, dots, and discolourations.
The higher the ISO, the more grain there will be.
It’s always a good rule of thumb to try to adjust your light source, aperture and shutter speed to gain proper exposure then adjust the ISO if the first three can no longer be pushed or it degrades the quality of the image to unacceptable levels.
If you’re curious about seeing the grain ISO creates. Take a photo of the same subject. One with a high ISO (more sensitive to light aka small bucket), and one with a low ISO (less sensitive to light aka bigger bucket).
Zoom into the image. Right up to the pixels and you should see a difference between the high and low ISO images.