To answer this question, you have to understand why the central bank targets a positive inflation rate in the first place. There are tradeoffs between high and low inflation. High inflation can reduce the real value of labor and is often more vloatile, but low values of inflation make cutting wages more difficult, particularly in recessions, reducing the demand for workers.
A lower inflation rate generally leads to lower interest rates because creditors demand inflation premiums when lending over longer periods of times. As those interest rates fall, the Federal Reserve has to lower their reserve rate (overnight lending to other banks). The idea is that the Federal Reserve has to try and give good rates so banks feel comfortable lending and being protected from liquidity crises. The nominal interest rate cannot fall below zero percent though, for obvious reasons (can't give away free money!)
So if the interest rate can't fall any further, we have a zero interest floor (ZIF) problem. The central bank will find it hard to encourage banks to lend out and increase the flow of money (which will usually then pump up inflation). So we get perpetually low inflation.
So why can't we just drop money from a helicopter to help alleviate the recession? After all, we learned from the Phillips curve that usually inflation and output are tradeoffs, right? And we want some inflation to encourage growth then, right? Well, outside of basic economics, it's a little different. One, it's illegal to just print money and create wanton seignorage (at least in America and most Western countries), and two, you run into the Lucas Critique of monetary policy. In a nutshell, if people expect inflation, inflation won't actually increase output in the short run. So dropping money is a very obvious way of increasing inflation that people will surely notice, and all you will have done is inflated the prices of goods and not done anything to help move out of recession, risking stagflation.
So what should the central bank do? The major tool the central bank uses in case of hitting a zero-interest rate floor and having low inflation is quantitative easing. Basically the central bank buys huge amounts of financial assets from commercial banks and other financial institutions,as opposed to government short term bonds. So the price of those assets rise, their yield falls, and the money supply increases. If that doesn't work, there is always price level targeting, although it hasn't been used a whole lot (yet). The idea is that the central bank, instead of committing to targeting inflation for every period, it promises to target a price level as if there was that "optimal" amount of inflation every period.
Targetting inflation is usually important because of Ramsey's time-inconsistency problem. If Lucas's Critique is right, then the Fed should have an incentive to lie about what inflation they will target, in order to increase output, but then they will lose credibility and lose all power to conduct monetary policy. So the central bank commits themselves to targeting one level of inflation--or in times like these, perhaps price level.