A great circle is defined as a circle on the earth's surface the plane of which passes through the centre of the earth.
For navigation purposes :
The great circle track is the shortest distance between two places on the earth's surface.
The great circle track appears as a straight line on Gnomonic (great circle) charts.
The vertices of a great circle are the two points nearest to the poles which have a course on the great circle track due EAST / WEST.
To follow a great circle track, the navigator needs to adjust the ship's course continuously because the great circle track is a curve when plotted on a Mercator Chart. Therefore, it is not really practicable to sail on an exact great circle route.
In order to take advantage of the shorter steaming distance of the great circle track, mariners usually divide a great circle track between the initial position and the destination into smaller segments (way points) of about one to two day's steaming time and make course adjustments at noon. The total distance is therefore the sum of the distances of those segments calculated by means of Mercator Sailing.