The 2% level is rather arbitrary, but the basic idea is to set a small positive number because it is a lot easier for central banks to fight inflation (a rising price level) than for them to fight deflation (falling prices).
The reason is simple: to fight inflation, it can slow spending by raising interest rates and increasing the cost of borrowing. More importantly, a central bank can increase them as high as it needs to. For example, Federal Reserve chairman Paul Volcker fought inflation in the 80s by raising rates close to 20% (which seems like a lifetime ago in this era of ultra-low rates).
How to Fight Deflation?

To fight deflation, a central bank can lower rates, but a huge problem occurs when they get down to 0%.
While it is possible to lower rates below 0% (Europe currently has negative interest rates), the effect isn’t nearly as powerful because most people will rather hold money in cash than pay interest to a bank on their savings.
This is known as the “zero lower bound” problem as mentioned by Bernard Mc Alinden.
Can You Escape a Liquidity Trap?
Both inflation and inflation can sow the seeds for their continued existence if they persist too long. If people expect prices to rise (inflation), they will want to buy earlier to get the lower price before it rises, and the higher rate of spending increases demand and causes prices to rise even more.
Conversely, if they expect prices to fall (deflation), people will hold off on buying because they expect to be able to get a better deal later, and the lower demand causes prices to fall.
This is known as a liquidity trap, and for an idea of how difficult it can be to escape, refer to Japan’s “Lost Decade” in the 90s.
What Can You Expect?

Economies are very large and complex phenomena, and so monetary policy has a rather long and variable lag before its effects can propagate throughout an economy. Indeed, it’s rather akin to steering a very large and heavy ship.
As such, central bankers want a margin of error in order to be more comfortable in avoiding deflation (i.e., they want to give icebergs a very wide berth).
That’s the main reason, but for a couple of others, see this article from the Federal Reserve Bank of St. Louis.
Originally posted at Quora.