I had some better graphics to help get my kids' heads around this, but can't seem to find them (the graphics, not the kids' heads). This'll have to do... ( I didn't have an apple or a rubber band, so I had to opt for this approach.)
Imagine Cathay Pacific is enroute from Los Angeles to Hong Kong. On a Mercator projection (flat map) the route might look curved, like this:
However, if you were to look at that same route plotted on a globe, it might look more like a straight line, like this:
Same route, different view.
I, for one, think it is magic.
Dave