There are a number of sources of noise contamination.
Heat generated might free electrons from the image sensor itself, thus contaminating the "true" photoelectrons. These "thermal electrons" give rise to a form of noise called thermal noise or dark current.
Another type of noise is more akin to the 'grain' obtained by using a high ISO film. When we use a higher ISO, we are amplifying the signal we receive from the light photons. Unfortunately, as we amplify the signal, we also amplify the background electrical noise that is present in any electrical system.
In low light, there is not enough light for a proper exposure and the longer we allow the image sensor to collect the weak signal, the more background electrical noise it also collects. In this case the background electrical noise may be higher than the signal.