1. When a cat wants its owner to play with it, it may purr while circling around its owner's feet;
2. When a cat feels safe and relaxed in a familiar environment, it will purr involuntarily. 
3. Some cats may purr when they stretch, which is actually a sign that the cat is very comfortable;
4. If your cat purrs continuously for a long time, it may be a symptom of a respiratory infection. It is recommended to take your cat to a veterinary hospital for examination as soon as possible.