Only the smaller cat species such as the domestic cat can purr. Cats that can roar, such as lions and tigers, can’t do it! It is thought that purring is due to the vibration of the larynx and vocal chords. Check to see if you can tell that your cat can do this while breathing both in and out.
Cats usually purr when they are content, but also may purr when anxious or in pain. If your kitty is purring at the veterinary office it is probably due to anxiety! There is even some evidence that purring can boost healing in both cats and their human counterparts.
It is thought that cats developed purring as a signal between a mother cat and her kittens.
Check out this page about the other feline vocalizations.
Further Reading:
Why Do Cats Purr? (NC State Veterinary Medicine) – NC State University College of Veterinary Medicine Behavior Expert Explains.
Everyday Mysteries (Library of Congress) – Why and how do cats purr?