Is there an explanation for why a horse that is perfectly sound with bare hindfeet, would actually move better when hind shoes were applied?

I recently put hind shoes on my horse - which had no real need for them - his feet looked great; but, we were going on a trail ride where the footing was going to be fairly difficult. So I had hind shoes put on him.

In our next lesson (before the actual ride), the difference in his movement was obvious. He seems so much more powerful and lighter in the front end.

This is not at all uncommon. Despite our experience and expertise, there are still things that we cannot see, and the horse cannot tell us. The feet may have looked great, but if the horse was better with shoes, the feet were probably not as good as they looked. If your horse does better with the hind shoes, I would just be happy and keep his hind feet shod.

I figured the answer was going to be as simple as that. Thank you for your time.

Horses are "rear- wheel-drive" vehicles. They power off their hind legs. If you give them all the traction up front, by shoeing just the front end, they start pulling themselves from the front rather than pushing from behind. They are then trying to lift the front end while dragging themselves forward. Try getting down on all fours yourself and pulling yourself forward with your hands as opposed to pushing yourself forward with your hind legs. You'll get the idea.
Also, people who shoe horses with square toes behind are taking away a lot of the purchase of the toe on the hind feet and decreasing the power the horse gets from his hind feet. (Just a little side note that is somewhat related.)

The main purpose for shoeing any horse is to protect its feet. It is, however, a nessasary evil. Putting holes into a hoof weakens the wall. The extra weight causes the foot to fly differently. If not done properly can cause lameness. likewise can prevent lameness. Depending on a large number of variables a competent farrier might choose to alter a shoe beyond that of the shape of the hoof. Ask plenty of questions, listen to answers. As for my horses, currently five, between the ages of three and ten, have been never been shod.