Meaning
'It belongs to / it's for' — a construction combining 'a' (it is) with 'fi' (for, belonging to) to mark possession. 'A fi mi dat' means that's mine, and 'a fi who dis?' asks whose is this. 'Fi' is the Patois possessive and purpose particle, so 'fi mi book' is my book and 'fi him yard' is his yard, and set behind 'a' it makes the plain statement of ownership. Among the small but essential grammatical building-blocks of the language, 'a fi' does the constant work of saying to whom a thing belongs.
Examples
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A fi mi dat, nuh touch it.
That's mine, don't touch it.
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A fi who dis book?
Whose book is this?
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Di land a fi di whole family.
The land belongs to the whole family.
Origin
'A' (it is) plus 'fi' (for/belonging to, the Patois possessive-and-purpose particle) — marking ownership.
How it’s used
Marks possession ('a fi mi' = mine, 'a fi yuh' = yours). 'Fi' also means 'to/for' before verbs ('fi eat' = to eat).