Meaning
Greedy and grasping — above all for food or for anything free. A 'licki-licki' person eagerly grabs at whatever is going, without shame or restraint, quick to lick up every crumb and press for more. The doubling of 'lick' pictures the eager, repeated licking of a greedy mouth, and the word sits with 'craven', 'greedy', and 'gravalicious' in the rich Jamaican vocabulary for the undignified hunger of those who cannot hold themselves back.
Examples
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Nuh be so licki-licki, wait yuh turn.
Don't be so greedy, wait your turn.
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Di licki-licki bwoy tek two plate.
The greedy boy took two plates.
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Free food bring out di licki-licki inna people.
Free food brings out the greed in people.
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Di likky-likky bwoy always a beg food.
The greedy boy is always begging for food.
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Nuh be likky-likky, wait till dinner ready.
Don't be greedy, wait until dinner is ready.
Origin
A reduplication suggesting eager licking and grabbing; the doubling stresses the grasping, greedy behaviour.
How it’s used
Disapproving, close to 'nyami-nyami' and 'craven', with a special edge of shameless grabbing at freebies.