If something is convoluted, it's intricate and hard to understand. You'll need to read over your brother's convoluted investment scheme a few times before deciding whether or not to go in on it.
Convoluted comes from the Latin convolutus for rolled up together. Its original meaning in English was exactly that, first for eaves coiled up on themselves, then for anything rolled or knotted together. Over time convoluted took on its metaphorical sense of complicated and intricate, which is how it's generally used today. People complain about convoluted legal language and the convoluted tax code.