Meaning
To insult, mock, or diss someone — to show them up or put them down in public, often in a song, a boast, or a piece of dancehall clashing. 'Him style mi inna di lyrics' means he dissed me in his lyrics, holding me up to ridicule. To 'style' a person is to make sport of them with a clever, cutting turn, and it belongs to the sharp, competitive art of verbal put-down, where the wittier and more wounding the styling, the greater the victory.
Examples
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Di deejay style him rival inna di tune.
The deejay dissed his rival in the song.
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She style him inna front a everybody.
She mocked him in front of everyone.
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Nuh mek dem style yuh.
Don't let them show you up.
Origin
A Jamaican extension of 'style' — to put a certain 'style' on someone, that is, to characterise or brand them mockingly.
How it’s used
The 'diss/mock' sense is distinct from ordinary 'style' (fashion). Big in dancehall clashes, where artists 'style' each other.