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. Algorithms like Kruskal's algorithm and Prim's algorithm are commonly used to find the minimum spanning tree of a graph. These algorithms systematically select edges based on their weights, ensuring that no cycles are formed, ultimately resulting in an efficient way to connect all points with the least cost.