Try out a few examples for practice. It is a useful concept in the field to help locate yourself. Dealing with a spherical Earth. A straight line on a flat map is not the shortest distance between two points on a spherical surface such as the earth. This is a great circle route.
Compass direction varies constantly.
Great circle routes are important to navigators calculating lengthy trips, e.g., trans-oceanic flights or voyages because they are the shortest routes. It is difficult to portray great circle routes as straight lines on map projections. The gnomonic projection works but is limited to less than a hemisphere. Nowadays, computers can calculate these routes fairly easily. His projection provides constant directions at each meridian on the map.