Each CCD has millions of pixels sensitive to brightness (Well you know how many, you can't miss that: 3.3 MegaPixel etc..). These pixels are on a very small space. In consumer cameras this would be from 8 mm to half an inch. (Nice mixture of measures:-)
These pixels are never the same and each of them has different charge leakage rate.
If you expose the CCD long enough, the pixels thanks to this leakage will simply lighten up even with no light. (Any photosensitive silicon material is sensitive to charge as well)
Because of different quality and sensitivity of each pixel, they will start appearing as a noise - but if you would able to expose for much longer, finally all pixels will lighten up.
HotPixels Eliminator will successfully remove most of the HotPixels traces. You could also use Dark Night Shots option to remove additional "blue" noise chunks. These will appear in extremely long exposures (6-8 sec).