Difference between vertices and edges

Vertices are the dots, edges are the lines. Hence cities and roads.

Here,
Cities are stable like dots.
Roads are the lines from one city to another.

So cities are used as vertices and roads are used as edges.

Another:
Vertices are the nodes of the graph. Edges are the arcs that connect pairs of nodes.

Resource Link: 
Difference between vertices and edges [Graphs, Algorithm and DS]