Proofiness. Zero is similar to A Brief History of Infinity, by Brian Clegg, in that it's more of a history book than it is a math or science book. They're also similar because they talk about infinity, because zero is "infinity's twin."
The first six chapters of Zero (or the first seven, depending on how you count them) are about the idea of nothing slowly working its way into the mainstream, followed closely by the idea of the infinite. There was actually a lot of resistance to both of these ideas, especially in the West, which is made even more interesting by Seife's flowery writing. I'm not entirely sure what "flowery writing" actually means, but I'm pretty sure it happens in this book. Zero does technically go into some math, but never in much detail. There's just enough math to make sense of all the pretty pictures.
The last three chapters are about zero in physics, where it likes to cause problems. This second part seems much weaker than the first part; Seife uses quite a bit of hand-waving, and never shows us a single equation. I think that if Seife would show us the actual equations and where the zeros are, we would better understand why zero is to blame for these quirks. That said, I'm sure some people will be glad that the math all but disappears when the physics comes on.
If you wonder how ideas take hold, or like history, or are somewhat confused about zero yourself, then maybe give Zero a try. For what it's worth, I finished it in just three days, so it can't be all that boring. (Although, that probably says more about my schedule than it does about the book.) I think the best way to understand what Zero is like is probably just to read the introduction (which Seife calls "Chapter 0"), so I've just typed it up here. This might be illegal. Don't tell anyone. The point is, he remains that flowery throughout the book, and if you like that section, I think you can enjoy the rest.