It's probably one of those things people end up memorizing, when learning about lenses or 3d figures like polyhedrons. It's like latitude and longitude. You can try to derive meaning from e.g. "lat = lateral", but then, do the lines go across or are they measuring distance across (which would make the lines vertical)? Either you memorize the correct answer, or you can easily get mixed up by over-analyzing the meaning.

concave -> (cave, cavity) -> hole

convex, you sort of just have to memorize. As best I can tell from introspection, I've associated the sound/visual of "vex" with "outward"