Here's how to explain it. When you send a box of glasses in the mail, you write fragile on the box. When you send something robust, you write nothing. So robust isn't the opposite of fragile, as some might suppose. The opposite of fragile is something that gets stronger when it's broken—something antifragile.
It's a useful word for many reasons, but I'm primarily interested in how it applies to politics because it allows us to bypass many typical (boring) partisan arguments about whether regulation is inherently good or bad.
Taleb starts with the premise that we will never eliminate volatility (i.e. Black Swan events, or random unforeseen changes). From that premise it follows that we should only pass regulations which will make the economy more antifragile (that is, stronger after the inevitable future volatility).
That may sound simple-minded, but the implications are important. For instance, this rule of thumb would eliminate endlessly complicated regulation like the Dodd-Frank Act (which may eventually sprawl to 30,000 pages of rules—creating loopholes ripe for cronyism), but it would leave open the possibility for simple, market-wide regulations like breaking up the banks, or banning credit-default swaps.
In other words, an antifragile economy is one that implements only regulations that aren't needlessly complex, don't pick winners and losers, and never add hosts of bureaucrats. By this token an antifragile economy also favors diverse, simple, small and medium-sized governments over the concentrated hive of bureaucrats that Washington has become. (Taleb's uses early America and Switzerland as models to follow, and I agree.)
What's more, an antifragile economy is full of entrepreneurs and small/medium-sized businesses instead of megacorporations. We know that entrepreneurs fail frequently, over and over, but each failure makes the future economy stronger as it quickly learns from their/our mistakes (thus, it's antifragile). This is the opposite of "too big to fail," a system where each recurring failure weakens the future economy for years to come, with losses spilling over to unrelated parties (i.e. taxpayers).
So here's a word that breaks the pro-regulation/anti-regulation dichotomy: antifragile. It provides us with a useful rule of thumb, a new and better way to frame debates about the intersection of business and government. It's a word we should start using.
Here's a link to an interview with Taleb from a year ago that I've listened to (perhaps embarrassingly?) more than half a dozen times. You can get a feel from the interview about whether you'd like the book (which is divisive and admittedly off-putting to some people).