Air Vibration
The most likely hypothesis concerning the physical phenomena that causes cat purring is that muscles in the cat's larynx (in the throat) and diaphragm (in the chest) alternate signals to begin vibration. As the cat breathes in and out, the sound of rapid dilation and constriction of the cat's glottis (vocal cords and the space between the vocal cords in the larynx) is what people recognize as purring.
Contentment
Cats begin purring as kittens and they hear their mothers purr back at them. This comforting sound may also be a means to communicate to each other. The mother is calming her children and asking if they are all right and the children are answering by expressing their contentment. This contentment later transfers to the owners, who can elicit purring by petting, snuggling with or even just greeting their pet cats. Although purring is likely involuntary, cats are very likely expressing contentment by purring when their behavior suggests that they are happy and healthy.
Duress
Perhaps most confusing for cat owners is the fact that cats purr when under duress as well, so that there is no way to prove conclusively that cat purring is an expression of contentment. However, purring may be slightly different under duress; in any case, other components of behavior-such as hiding, shedding fur and a loss of energy-indicate that the cat is not happy even while purring. Some researchers have hypothesized that purring while under duress-when being brought to the vet's office, for example-could be related to the cat's purrs while contented. Desiring no harm (or further harm) to come to it, the cat is expressing a sentiment akin to "I mean no harm, so don't harm me" or "I am all right, so please leave me alone." Other researchers have a different theory to explain purring while distressed that involves a healing mechanism.
Potential Healing Powers
Although this hypothesis has not been proven, veterinary scientists have been exploring the theory that cat purring offers the cat some sort of healing mechanism; this would explain why cats purr when sick or injured while clearly not happy. Studies have shown that sounds in the 25 to 150 Hertz range (the range of purring) may improve bone density and encourage healing in the body. Scientists are further exploring this phenomena by using similar sounds to promote human healing and bone density (a problem in long-term astronauts, for example).
Although the exact reasons behind cat purring are still unknown, what is clear to experts and animal enthusiasts alike is that purring represents strong emotions, both positive and negative. Cats both show affection and express distress while purring and the other behavior of the cat can help explain why cats are purring at any given time.