Meaning
To meet or run into someone by chance — to bump into them unexpectedly — and also to knock or stub against something. 'Mi buck up pon him inna town' means I ran into him by surprise, while 'mi buck up mi toe' is I stubbed my toe. Built from 'buck' (to butt or bump), the phrase covers both the happy accident of a chance meeting and the sharp knock of striking against a thing, and it is among the most everyday ways of describing an unplanned encounter.
Examples
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Mi buck up pon mi ole friend a town today.
I ran into my old friend in town today.
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Mi buck up mi toe pon di stone.
I stubbed my toe on the stone.
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If yuh buck up pon di answer, let mi know.
If you happen to come across the answer, let me know.
Origin
From 'buck' (to butt or knock against) plus 'up' — to knock into, hence to meet by chance.
How it’s used
Chiefly 'buck up pon' = to meet by chance; also literally to knock/stub against something.