Let's take the city where you live in. Take any two bus stations, namely A and B, and the entire commuter network. This network is a graph. Stations are nodes, commuter connections between stations are edges (edge weight = time it takes the bus to travel between two stations).
Say, you want to travel from A to B in the shortest amount of time possible (you wont want to waste time, would you?).
Dijkstras Algorithm has as input the graph representing the commuter network and the node A and is able to deduce the shortest path from A to any other station (which includes the shortest path from A to B).
Does that help you? Wikipedia on Dijkstra has more detailed examples.