Any line bisecting the surface of a sphere into two equal halves.
The shortest route between any two points on a sphere (or globe), also known as an orthodrome (roughly, "true course"), lies on a great circle.
While there are an infinite number of possible great circles on a globe, familiar examples are the equator, oriented east-west, and the meridians (of longitude), oriented north-south. Generally, however, the azimuth of any great circle route connecting two points varies throughout its path.
(Compare with rhumb line.)