In tree connection, spanning tree means that all nodes of a graph to be connected with each other either directly or indirectly. Minimal spanning tree problem is then a spanning tree graph that weight less than or equal to the weight of every other spanning tree graphs.
Each node is propotional with weight which is proportional to length. Source:Wikipedia
To visualize, one can imagine how Telecommunication Company would use cable to connect each individual residential building. It would use cable in unidirectional fashion and with shortest path.