The one we're most familiar with is the demand meow, which means "I want to be fed" or "I want to go out" or "Pay attention." There are also meows that are pleading, which can often start with a soft purr, a purr-meow. And then there's caterwauling which is usually an aggressive call between two male cats.
She says there's also a hunting meow and a kind of trilling meow mother cats use with their kittens. So meows are a versatile form of communication. Purring, on the other hand, is simply a sign of comfort. Dr. Houpt says that unlike meowing or human speech, purring isn't the result of air passing over the vocal cords. It's a vibration of the larynx that resonates down to the windpipe and into the diaphragm. Kittens use it to communicate quietly with their mothers while they're nursing.
http://www.sciencenetlinks.com/sci_update.cfm?DocID=11