Whenever you are attacked by a vampire, you run the risk of being infected with Sanguinare Vampiris. Initially, this is a normal disease that reduces your total health by 25 points. It is subject to the rules which govern any other disease, and can be cured in the same fashion. However, not curing the disease within three days will cause it to progress to full vampirism. At that point, the effects can no longer be reversed with a normal cure.
You have some powers you can use, these get better if you starve, and you'll get more powers as it happens. The drain health spell you get is handy too.