We all know that racing drivers overtake on the inside — it's the shorter, faster route. It was only relatively recently that I've found how useful it can be on a long drive too, not for racing, but for using the bend on a multilane road for easier, safer overtaking.
Perhaps this scenario will resonate: after cruising at a steady speed for miles of a long journey you slowly catch up with a car traveling just a few miles an hour slower. You're not driving fast enough to zip by them, but the difference is enough to slow your steady progress on a long journey, and if you're driving near the speed limit anyway you probably don't want to accelerate much to overtake.
On a multi-lane road like a motorway or freeway — not a single lane road where you'd be overtaking with reduced visibility on the corner in the opposing lane — timing your overtaking so you're on the inside of a bend and the slower car is on the outside allows you to get round the slower driver in a shorter time and without needing to travel nearly as fast.
And the converse is also true: if you've timed your overtaking when approaching a bend where you'll be on the outside you'll find that you'll have to go a lot faster to get round or perhaps that your intended overtaking is actually not getting you past at all.