Purr

Cats can produce a purring noise that typically indicates that the cat is happy.  Less typically it can also can mean that it feels distress. Cats purr among other cats—for example, when a mother meets her kittens. There were many competing theories to explain how cats purr, including vibration of the cat's false vocal cords when inhaling and exhaling, the sound of blood hitting the aorta, vibration of the hyoid apparatus, or resonation directly in the lungs. But currently, it is believed that purring is a result of rhythmic impulses to the cat's larynx.

Video - This is not exactly a friendly cat purr

Purring may also be a way for the cat to calm itself down. For example, some cats have been known to purr when hurt. Though not proven, research has suggested that the frequency of the vibration produced by purring may promote healing of bones and organs in cats, explaining why cats may purr when hurt.