There are those who claim the horse's back does not really flex laterally. Watch this video.
When you are sitting behind your horse in a carriage, the back, from it's tail all the way up to the poll, should look like a fish swimming through water *if* all the parts are moving freely and correctly. If that is not the case, it's probably time to enlist a chiropractor, acupuncturist, farrier and vet.
It should look something like this from behind: