One of the core concepts of the book is 'matter compilers'–the idea that you can combine individual particles to create something new. This concept is never fully explained, but there are certain aspects of matter compilers which are limited (e.g. you can't synthesize fish or other organic compounds).
The core part of the name comes from the idea that, like the bronze age or iron age, we can manipulate atoms at will to form diamonds.
Perhaps the more interesting part of the book (to me anyway) is that it details an idea for interactive education, via the "primer".
The primer is suited directly to its owner, in the book it's Nell. It works via a set of stories, and can't help but remind me of PG's early words in YC: stories are powerful. Maybe they're even the best way to learn.
Nell can customize the primer to her liking, it teaches her to read by first speaking to her, but gradually she mutes it to transition to reading outright.
The stories themselves are strange (and memorable!), in sort of the same way that the stories in Exhalation are. They revolve around a set of dinosaurs, who stumble upon an all-powerful rat named Dojo.
Dojo teaches the main characters in the book various aspects of combat, and Nell begins to pick those up herself via repetition and observation. It's another instance of "showing someone how to do things" being unreasonably effective.
The other interesting thing about the primer is that it's totally generative. I'm reminded of the "open world" adventure games, like Minecraft or No Man's Sky. When you imagine something and start to ask about it, it's there!
The primer is part NPC-like characters, but also part "ractive" (short for interactive). The idea here is that humans come together to generate plays that are interactive, but they are different each night as the human actors change and grow. With new language models, I wonder how rich you could make these dynamic worlds on-demand with infinite possibilities, but still apply some subset of rules.
The primer teaches Nell (the protagonist) everything from self-defense to how to program computers. Each new 'kingdom' or 'level' involves some sort of quest to unlock a set of keys as Nell learns new skills.
Overall, the book reminded me a lot of Snow Crash in terms of its themes, environment, and mix of old-and-new. In some ways, I think the technology mentioned is actually more interesting, even if it's more different than what we have today.