A spanning tree of a graph is a subgraph that connects all nodes using exactly n−1 edges, where n is the number of nodes. No cycles allowed. If you have 5 nodes, the spanning tree has exactly 4 edges. Add one more edge and you create a cycle.
Remove an edge and the graph becomes disconnected. Think of it as the skeleton of the graph. Minimum edges, maximum connectivity. This is the foundation for understanding MST.