It's when you refer to someone as 'she' while they're actually present. The polite thing to do is to refer to them by their name.
'She is the cat's mother' is saying 'you don't use the word 'she' for someone that is present. You would only use 'she' for a person who isn't present, or a creature that doesn't have a name. Your cat probably has a name, so you wouldn't normally use 'she' even for your cat. You might use 'she' for the cat's mother, though, since the cat's mother is probably deceased by now, or maybe you got the cat from somewhere else and the cat's mother was never part of the household.'
That's roughly what 'She is the cat's mother' means, I think, but the reality is, it's just what people traditionally say to rebuke someone for saying 'she' when they should have used the person's name.