Kruskal's algorithm is a method used in graph theory to find the minimum spanning tree of a connected, weighted graph. It works by sorting all the edges in the graph by their weights and then adding the smallest edge to the tree, provided it doesn't form a cycle. This process continues until all vertices are connected. The algorithm relies on the concept of disjoint sets to efficiently manage and check for cycles. By using a union-find data structure, Kruskal's algorithm ensures that each edge added maintains the tree's properties, ultimately resulting in the minimum total edge weight for the spanning tree.