The zero lower bound (ZLB) has moved from a theoretical possibility in the 1980's to a modus vivendi in the 1990's Japan, the late 2000's US and the 2010's Eurozone. The ZLB does not mean that the interest rate is necessarily at zero, but it does mean that it has reached a low beyond which it cannot fall. The problem with this situation is that monetary policy, as is commonly practiced by manipulation of the interest rate, becomes inefficient as, by definition, the interest rate cannot fall any further to accommodate for declining demand. This situation challenges policies and ideas in the economics profession as, over the last 50 years and with the prevalence of monetarism as the world's leading school of thought, economists believed that just controlling the interest rate could cure every recession possible.
It does not; the problem with the ZLB is that, just like any other activity which involves agents and forecasts, it becomes embedded in expectations. That is, if people see the interest rates not being able to fall further, they believe that the situation will be continued in the near future, which means that base their decisions on that, making the ZLB a self-fulfilling prophecy. The issue here is that the ZLB does not just mean that interest rates are low; it comes with an additional problem the one of dis-inflation or, in extreme cases, the one of deflation (Frances Coppola has an excellent article on why deflation is something we should worry about).
In addition, the ZLB does not come alone, but brings its friends along with it: low interest rates mean that even though most banks can they are unwilling to lend and, as if that wasn't enough, most businesses are unwilling to borrow. Even if the rates are low, people are still unwilling to spend due to the simple reason that they expect the situation to remain unchanged in the future; with spending being low and the overall money supply either contracting or just slightly increasing why should they assume the risks? This is the situation we have been experiencing in the Eurozone over the past year (the large change in M1 is just an outcome of the shift from long-term deposits to overnight deposits):
The only remedy for the situation is what has been known as unconventional policies: QE, OMT and so on, yet these cannot be applied in the Eurozone at the moment. In addition, increased government spending is a midsummer night's dream in most countries, which are tormented by bail-out agreements forcing tight budgets, meaning that it's up to the ECB: either it does something in the next meeting, by which I mean a large boost package, or the situation will remain as terrible and uncertain as it is now.
And remember, uncertainty is always worse than bad news.