The Great Circle is a concept that takes awhile to understand, but then you'll never forget it. Now, the sliced orange analogy is overused, but it's a good one. Take a pen, mark two dots on an orange (not on the "equator" or straight up and down from each other on a "meridian" - as these are already "great circles"), and then slice the orange between the two dots with the knife angled toward the very center of the orange. If you were then to remove the peel in one piece and flatten it, what appeared to be a straight line on the orange becomes a curved line on the peel. So, the closest distance between two spots on a sphere is actually plotted as a long curve when using a flat representation - like a chart. Put simply: a mercator chart takes the curve out of the world, and you have to put it back in real life.
It is a difficult concept to fathom. There are many sites available to tell you great circle distance. Here's an example...great circle distance between Toronto to Hong Kong is 7810 miles (shortest distance). Many would think a straight line drawn would be shorter by going over California. If I calculated that route Toronto-San Francisco-Hong Kong it would be 9186 miles.
We could use the "polar routes" which fly over the "top." For a Toronto to Hong Kong flight, it shaves off one hour. It might not be the best great circle route but the winds are lighter over the pole. Coming back we tend to fly a more southerly route to capitalize on tailwinds further south.
Lots to think about when flight planning.
NEW*** Here's a link follower YYC Dispatcher sent: