Meaning
In Patois 'bad' swings two ways, and tone tells you which. Most strikingly it means the opposite of its English self: excellent, tough, formidable, impressive — a 'bad' player or a 'bad' tune is a great one, and someone 'bad' is not to be messed with. It also keeps the ordinary sense of morally bad, spoiled, or unwell.
Examples
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Dat DJ bad, yuh see!
That DJ is amazing, you know!
The praise sense.
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Him a bad man, nuh trouble him.
He's a tough/dangerous man — don't trouble him.
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Di milk bad, throw it weh.
The milk is spoiled — throw it away.
Origin
English 'bad', semantically flipped to praise (a common creole pattern). See [[wicked]], [[tallawah]].
How it’s used
Often means excellent/tough/formidable; also keeps the literal 'bad/spoiled/unwell'. Tone disambiguates.