I'm considering doing a review of this book. He did a presentation at a local book store, and he is an interesting and engaging speaker.
The core idea is that some modern systems are fragile. For example, an optimized supply chain will be lean, and the risk of a mismatch of inventory and demand is minimized, lowering cost. But, the lack of redundancy -- like a warehouse full of stuff -- makes this lean supply chain subject to significant disruption -- like after the Tsunami in Japan. Car production was disrupted in surprising ways around the globe.
The new idea is that some systems are anti fragile. That is, they benefit from volatility [or variance or risk]. And example is being long a simple call option, which becomes more valuable as volatility increases.
He explores the impact of volatility across a wide variety of situations.