A minimum spanning tree (MST) is a subset of edges in a connected, undirected graph that connects all the vertices together without any cycles and with the minimum possible total edge weight. This means that the sum of the weights of the edges in the tree is as small as possible while still maintaining connectivity among all the nodes. MSTs are useful in various applications, such as designing efficient networks, including computer networks and transportation systems. Algorithms like Kruskal's and Prim's are commonly used to find the minimum spanning tree in a graph, ensuring optimal connections with minimal cost.