The great circle distance is the shortest distance between two points situated on a sphere.
A great circle is a section of a sphere containing the diameter of the sphere. The GCD between two points is therefore equivalent to the shortest segment in between these points on the great circle that includes both points.
For two points situated on Earth, the GCD gives an approximation of the real shortest distance between these points because the Earth is not perfectly spherical (the Earth is in fact a flattened sphere : its radius changes according to the latitude).
More information to be found on : http://mathworld.wolfram.com/GreatCircle.html
Illustration of the Great Circle Distance
(Source : Weisstein, Eric W. "Great Circle." From MathWorld--A Wolfram Web Resource)
In the aviation sector, the distances really flown between two airports is more important than the GCD mainly because of the routes that have to be followed according to the existing beacons and congestions at airports that force aircrafts to turn a certain time around their target before being authorised to land.
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