All cats will bite at their own fur on a regular basis as a part of their grooming behaviour, but it can also be a sign of irritation of the skin. A cat sitting calmly that suddenly turns and bites itself probably has an itch.
By far the commonest reason for cats biting themselves is fleas. Any cat that goes outside, and some which do not, are likely to pick up fleas. Treating your cat regularly against fleas with a product recommended by your vet is advisable, even if you cannot see any.
Some cats will cause their skin damage by biting. This usually shows up as multiple small scabs around the head and along the back. If this occurs the cat is allergic to something. The biggest cause of allergy in cats is fleas (about 99% of cases).
Some cats will bite themselves for psychological reasons, if they are scared or stressed much of the time. The appearance is often similar so it is always worth ensuring fleas are not the problem first.
This pet health article is for reference only.
If your pet is showing any symptoms or distress, and you suspect your pet is ill CONTACT YOUR VET IMMEDIATELY.