王八 originally means turtle/tortoise, long a symbol of cuckoldry in Chinese folk culture (turtles were thought to be fathered by snakes, hence 'illegitimate'). 王八蛋 - 'turtle egg' - is thus an insult about one's parentage, equivalent to 'bastard'.
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Strong insult between adults. Softer than 操你妈 but well past polite - avoid in formal or professional settings.
