Meaning
A bald or clean-shaven head, or a person with one — 'egghead' pictures the smooth, egg-like dome of a bald head. Usually teasing. (It can occasionally carry the other English sense of a bookish, brainy person, but the bald-head sense is the everyday Jamaican one.)
Examples
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Since him shave, him a real egghead.
Since he shaved, he's a real baldy.
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Di sun shine pon him egghead.
The sun shone on his bald head.
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Dem tease him bout him egghead.
They tease him about his bald head.
Origin
From the smooth, egg-shaped look of a bald/shaved head.
How it’s used
Chiefly a bald head/baldy (teasing); can rarely mean a bookish person. Compare 'shine head', 'baldhead'.