Cats purr when they are content, but they may also purr when they are feeling anxious or stressed. When a cat purrs and then bites you, it could be a sign that the cat is feeling overwhelmed or threatened. It is important to be aware of the cat's body language and look for signs of stress or anxiety. If the cat is feeling threatened, it is best to give it space and allow it to relax before attempting to interact with it again.