Convex duality is a way of looking at problems that involve two sets of data (called a 'dual' problem). It can help us to understand what the best solution is and how this solution relates to the two sets of data. Think of it like two puzzles. Each puzzle has its own pieces (set of data) and you need to find the best way to fit them together. The convex duality helps by looking at the two sets of data and determining what the best answer is, and how it relates to the two sets of data.