Berge's Theorem is a result in combinatorial optimization that deals with the properties of matchings in bipartite graphs. It states that if a bipartite graph has a perfect matching, then every subset of vertices on one side of the graph can be matched to a distinct subset of vertices on the other side. This means that there is a way to pair elements from two groups without any overlaps. The theorem is significant in various fields, including graph theory and economics, as it provides a foundation for understanding how to efficiently pair items or individuals. It helps in solving problems related to resource allocation and network flows, ensuring optimal matches between two distinct sets.