Given an undirected weighted graph, a minimum spanning tree (MST) is a subset of the edges of the graph which form a tree and have the minimum total edge weight. For a MST to exist, the graph must be connected (that is, every pair of nodes must be reachable from each other).
Example of Minimum Spanning Tree. Total edge weight = 5 + 8 + 8 + 4 + 11 + 6 = 42
Kruskal's algorithm build's the minimum spanning tree one edge at a time. To see what that means, watch the following video.