"From concentrate" simply means that something is extracted from a certain source, by squeezing to produce a concentrated syrup. "Not from concentrate" is the opposite. "Not from concentrate" products are usually more expensive than "from concentrate" simply because they have superior flavor; they are the best.
From concentrate has been processed more and basically made a lot stronger to be diluted with water later. Not from concentrate is basically freshly made or squeezed fresh in the example of orange juice. not from concentrate is supposed to taste better because it is fresher.