Meaning
Beyond the taste, 'sour' describes a sulky, bad-tempered, or spoiled mood — a 'sour face' is a scowl, and 'him a gwaan sour' means he's being surly and unpleasant. It can also mean that a plan or a situation has 'gone sour', turned bad and curdled. So the word runs from the sharp taste to the soured temper of a sulking person and on to the whole affair gone wrong, all sharing the sense of something turned off, spoiled, and no longer sweet, whether a fruit, a mood, or a matter.
Examples
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Why yuh face suh sour today?
Why is your face so sulky today?
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Di deal turn sour pon dem.
The deal went bad on them.
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Him sour because him nuh get him way.
He's in a bad mood because he didn't get his way.
Origin
A figurative extension of the taste 'sour' to a soured mood or a spoiled situation.
How it’s used
Means sulky/bad-tempered ('sour face') or gone bad ('turn sour'), beyond the literal taste.