Kőnig's theorem is a fundamental result in graph theory that relates to bipartite graphs. It states that in any bipartite graph, the size of the maximum matching is equal to the size of the minimum vertex cover. A matching is a set of edges without common vertices, while a vertex cover is a set of vertices that touches all edges in the graph. This theorem is significant because it provides a way to find optimal solutions in various applications, such as network flow problems and scheduling. It highlights the deep connections between different concepts in graph theory, making it a key tool for mathematicians and computer scientists.