Intuitively, the shortest distance between two points is on the straight line joining the two points.  But this is true only if one is travelling on a plane surface.

In fact, it depends on the shape of the surface you are travelling on. If you travel on the surface of a sphere, for example, the shortest route between two points lies on a geodesic or great circle. 

It depends on the shape of the surface

This is a circle on the sphere whose centre coincides with the centre of the sphere.

This explains why, for example, a plane travelling from Moscow to New York, which lies south of Moscow, starts off in the North direction, passes over Iceland, reaches the Southern tip of Greenland then starts moving south.  The diagram shows the approximate distances. 

This route, by the way, is also a good response to flat-earthers, who challenge the well-known fact that our planet is spherical.