Meaning
A euphemism for the female genitals — the softer, indirect stand-in for 'pumpum'. It is chosen precisely because it sounds harmless: it appears in lyrics edited for radio, in flirting, and printed on clothing where the blunt word could never go. The indirectness is a cover rather than a change of meaning. To anyone who speaks the language it is completely unambiguous, and it is still sexual.
Examples
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Dolly Kitty cute.
The shapely, attractive woman has a pretty 'kitty'.
A set phrase, and a good illustration of the problem: it reads as innocent to anyone who does not know that 'kitty' means the female genitals.
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Dem seh 'kitty' inna di radio version.
They say 'kitty' in the radio version.
The euphemism is what gets the lyric past broadcast standards.
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Watch how yuh use dat — a nuh puss him a talk bout.
Be careful how you use that — he isn't talking about a cat.
Origin
From English 'kitty', a cat, by the same euphemistic route that produced English 'pussy'. Jamaican usage keeps the cover but not the innocence.
How it’s used
Sexual, though indirect. It passes in mixed company far more easily than 'pumpum', which is exactly why a phrase built on it can look family-safe when it is not — worth checking before repeating a lyric or wearing a slogan you have not had translated.