The Great Circle is the largest circle that can be drawn around the Earth’s sphere. When cutting a sphere exactly in half you have cut along one of its great circles.
All Meridians are great circles.
The Equator is a great circle (i.e. cutting the Earth in half). Great circles are useful in planning routes as it depicts the shortest pathway between two points on the Earth’s surface (noticeable over long distances).
The Great Circle route follows the curvature of the Earth making it a shorter route (noticeable when doing greater distances) than a straight line drawn on a Mercator chart.