means Having the smooth, slightly slick, dull-shiny look or feel of wax, or in some dialects describing a sudden flash of irritation.

from From 'wax,' the soft modeling substance — itself from Old English 'weax,' the stuff bees build their combs from, a word with cousins all across the Germanic family (German 'Wachs,' Dutch 'was'). The '-y' simply turns the noun into 'wax-like.' The angry sense of 'waxy' is a separate, more recent and chiefly British slang twist, possibly playing on 'waxing' wroth — though that link is more folk-suggestion than settled fact.