What do cats mean? Does a cat’s purring mean anything? Of course it does. Your cat means something, and you will make what your cat purrs mean something anyway. Humans have an innate ability to impute meaning: to animal’s noises, to cloud formations, to weather systems, to patterns of stars, to a sequence of random events. We drive ourselves crazy reading more into the actions of people around us than we need to while driving other people crazy by not paying enough attention to what they actually say.
So what do cats tell us? They tell us nothing, but we always hear something. Cats no doubt mean things when they act or purr, but what we assume is always going to be the human-being-centred version.
A cat may be purring and I may be with her or him (as you see, I give my cats a gender they have never asked for), but this may be like when I sing in the bath and a bird looks on through the window.