Before the 1st century AD most writing was on papyrus & in scrolls, but each time you open a scroll the actual fabric that is written upon gets damaged. So once the idea of how to bind books was developed this took over as the standard format for preserving writing & knowledge. Bound books could also use parchment or vellum as their surface for writing (I think this is because if you have a long continuous roll then it's easier to make when using papyrus), and this is more durable in damp climates. And books are more easily put in one's pocket and carried about.
The next change that was mentioned was the putting of spaces between words - invented by Irish monks, apparently, to make it easier to learn to read a language than none of them were native speakers of (latin). And then we moved on to the development of paper, which was originally invented by the Chinese and came to Western Europe via Islamic Arabs. Paper is much cheaper and easier to make than parchment and vellum, and this made books more available to scholars. And once the material was cheaper mass production systems were set up to make more books more quickly - so one way this was done was to break a master copy of a book into sections and then give these to several different scribes, each would then write his part in a few days and the sections would then be bound together. Each copy was then made direct from a master copy so more accurate as well as much more quickly than one scribe copying out a whole work. One of the experts Bragg talked to pointed out that even though it's hard to tell from actual book prices what the effect was it's possible to tell by looking at the numbers of books people had. So in Chaucer there is a tale of a scholar who is very proud of having 10 books, but once these mass produced paper books were available even undergraduate students could have twice as many.
Then comes the printing press & the Gutenberg Bible. Printing again was an invention of the Chinese, several centuries earlier, and I'm not quite sure if the idea made its way to Western Europe or if this was an independent invention. But even if he got the idea from somewhere else the revolutionary thing was movable type, to allow you to do many different pages with the same equipment. And this then made books even more easily available (and cheaper again) than they had been. One of the experts refered to it as "the Internet of its day", meaning that it was as revolutionising to the society then as the Internet is to us in terms of ease of sharing of knowledge & scholarship.
It was a very Western centric episode, even though China and the Middle East were mentioned, it was only in relation to developments in Western Europe. So that seemed a shame, but there are still 3 episodes so they may redress the balance a bit.