Convexly tells you how something is shaped: it curves out, like the surface of the eye or the outside of a ball. It is an adverb, so it sits beside a verb or another describing word: the glass is convexly curved; the mirror bulges convexly. You will almost never hear it in the street. Scientists, maths teachers, and designers use it when they need to be exact. Everyday speakers just say “it curves out” or “it bulges.” It does not mean “in a complicated way” or “in a confusing way”; it only talks about that outward curve.