Mordell's Theorem states that the set of rational points on an algebraic curve of genus greater than one is finite. This means that if you have a curve that is complex enough (with a genus greater than one), you cannot find infinitely many solutions that are rational numbers. The theorem is named after the mathematician David Mordell, who proved it in the 1920s. It is a significant result in the field of number theory and has implications for understanding the structure of algebraic curves and their rational solutions.