One, the history itself is fascinating, even for somebody like me that's generally not a big history buff. (Perhaps it helps that the episodes are short!)
Two, the central conceit -- snapshots of history as told via examinations of various historical artifacts -- actually changed the way I look at things around me. Every single object we hold, mundane or otherwise, holds so much information and is shaped by so many things.
Here's one example I remember well: the famous "The Great Wave off Kanagawa" print. We tend to think of it as the most quintessential Japanese print. https://en.wikipedia.org/wiki/The_Great_Wave_off_Kanagawa
But it's more complex and interesting than that. It actually marks a big turning point in Japanese culture, as it actually incorporates major European influences: the rich blue inks and a European use of perspective to depict the mountain in the distance. So this unmistakably Japanese print represents a crossroads...
It's a tiny (but intricate) model of a chariot, rider and passenger, and yet through this, the program explains how it reveals the vast orderly road network of an empire, the functioning of a state and the diversity of its religions and regions.
wget -i <(curl -s http://www.bbc.co.uk/programmes/b00nrtd2/episodes/downloads.rss | grep -Po 'http://open.live.bbc.co.uk/.*?mp3' | sort | uniq)
It also seemed apparent to me that the objects were chosen based on their ability to reveal something unexpected. WWII is fairly well understood by most in the West at this point, at least when compared to some things that were explained in the Sharia credit card episode.
There are several billion Muslims in the world and Islamic beliefs prohibit moneylending for profit -- in other words, the charging of interest. That's something Jesus is depicted as opposing in the Bible, as well, so this is actually a bit of common heritage between Christian and Islamic cultures.
Yet the charging of interest is a practice so deeply ingrained in the Western financial system that we hardly think about it. When we learn that, it certainly makes us think about a few things. So I thought that was actually an excellent episode.
Wars have their own museum in London - the Imperial War Museum - and the computer revolution is somewhat represented in the Science Museum.