A spanning tree is a subset of a graph that connects all its vertices without forming any cycles. It includes all the vertices of the graph but only enough edges to maintain connectivity, ensuring there are no loops. Each graph can have multiple spanning trees, and the number of spanning trees depends on the structure of the graph. Spanning trees are important in various applications, such as network design and optimization. They help minimize the total length of connections needed to link all points, which is useful in fields like computer networking and transportation. Algorithms like Kruskal's and Prim's are commonly used to find efficient spanning trees.