Why do cats purr?

[Randi]

I've read that one of the reasons cats purr, is to tell they're not dangerous, that also explains why they purr when they're ill. However, I've noticed that our cat Fister purrs when he's content - or when he's coming up on our bed, waiting for a cuddle. But he has also been purring while ill.

[C.C.'s Mom]

I always thought that my cats purr to make me happy