Is the great circle route the shortest distance between two points?

Answer:

Yes, if you are talking about two points on earth's surface. The great circle can be thought of as roughly similar to a circle of longitude, or to the equator. It is the largest circle on the globe that can be drawn containing the two points in question. Why is this important? Consider the fact that the larger a circle becomes, the closer a section of the circle resembles a straight line. If you imagine a circle that is infinitely large, you would not be able to distinguish a section of it from a straight line drawn between the end-points. So when you have drawn the largest circle you can that contains two points on earth, you have come as close as you can to approximating a straight line between them (without digging).

To people who are not familiar with this idea, seeing a 'great circle route' drawn out on a Mercator projection seems impossible. Map projections have to sacrifice some important detail, because you cannot map a three-dimensional globe onto a two dimensional surface.