Kuratowski's Theorem is a fundamental result in graph theory that provides a characterization of planar graphs, stating that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of either K5 (the complete graph on five vertices) or K3,3 (the complete bipartite graph on six vertices, three of which connect to each of the other three). This theorem is crucial for understanding graph embeddings in the plane and forms the basis for more advanced topics in topological graph theory.