A great circle is a circle on the surface of a sphere that has the same diameter as the sphere. A great circle is the intersection of a sphere with a plane going through its center. A great circle is the largest circle that can be drawn on a sphere.
Great circle on a sphere.
Great circles are the "straight lines" (geodesics) of the sphere in non-Euclidean geometry.
The great circle on the spherical surface is the path with the smallest curvature and hence the shortest path between two points on a sphere. When intercontinental airline routes are drawn on a flat map (for instance, the Mercator projection), they often look curved. This is because they lie on great circles. A route that would look like a straight line on the map would actually be longer.