There are two possible answers - that depend on the context.
- In a concave polygon there exists at least one pair of vertices such that the line joining them lies wholly outside the polygon.
- Consider a hollow 3-d object whose body is made up of a material of some thickness. Then the distance between two points on the outside of the body will be grater than the corresponding points on the inside of the body. The outer points will define the external diagonal.
The second definition is sometimes used by airlines for cabin luggage. The outside shape of the case matters, not how big it is inside.
