Meaning
To screw up or wrinkle the face or nose in disgust, disdain, or displeasure. 'Skin up yuh face' or 'skin up yuh nose' is to grimace scornfully at something you find distasteful, offensive, or beneath you — a whole silent language of contempt written on the face. The gesture, drawing the features up in a sneer, speaks as loudly as any words, and to 'skin up' at a person or a thing is a plain, cutting show of rejection and disgust.
Examples
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She skin up har face wen she smell di food.
She screwed up her face when she smelled the food.
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Nuh skin up yuh nose pon di gift mi give yuh.
Don't turn up your nose at the gift I gave you.
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Him skin up him face like him vex.
He scrunched up his face as if he were annoyed.
Origin
From 'skin' (to draw or wrinkle back) plus 'up' — drawing the face up into a grimace of distaste.
How it’s used
Almost always of the face/nose, expressing disgust or disdain. Distinct from admiring 'skin out' (to dance).