Meaning
Extremely bad, tough, or fearsome — 'bad' here in the admiring dancehall sense of formidable and not to be messed with, as much as in the sense of wicked. 'Yaz' is yaws, a nasty, stubborn skin disease, so 'bad like yaz' means bad to a striking degree.
Examples
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Dat sound system bad like yaz!
That sound system is seriously formidable!
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Him drive bad like yaz — nobody cyaa test him pon di road.
He drives incredibly well — nobody can challenge him on the road.
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Di gyal talent bad like yaz.
The girl's talent is off the charts.
Origin
A simile drawn from 'yaz' (yaws), a persistent, disfiguring tropical skin disease once common in Jamaica — its severity lends the phrase its force. Note 'bad' in Patois often means formidable or excellent, not just wicked.
How it’s used
Usually admiring — 'impressively formidable' — though context can make it literally 'wicked'. Compare the dancehall use of 'bad'.