Functional MRI scanning has shown that areas of the brain normally involved in vision processing has been reallocated in such individuals.
Coincidentally, I've just finished reading a great book on this very subject: "Crashing Through: A True Story of Risk, Adventure, and the Man Who Dared to See", by Robert Kurdson. He describes Mike May's frustrations with not being able to read or process shadows to determine 3D information after having his sight restored, decades after losing it due to corneal scarring from chemical burns when he was 3 years old. Mike's restored vision - due to stem cell and corneal transplants, gave him better than average vision, but Mike found it extremely hard work to read or extract depth information from shadows. His ability to detect motion was excellent however. Curiously, Mike isn't fooled by optical illusions that take us in.
Unfortunately, depression has been found to be extremely common in people that have had their sight restored after a long period without it - most likely due to the frustrations of not being able to fully use their restored vision.
Mike needed donor stem cells and cornea, whereas this improved technique uses the patients', thus avoiding the risks associated with taking anti-rejection medication for life. Now if only we can find a way to restore brain function! That would be an incredible breakthrough helping far more people than those assisted by this new technique and would hopefully help with the depression risk. There are some interesting references in the above book, which include the article by Oliver Sacks referenced above.