Inflation targeting is a policy whereby a central bank publicly announces an explicit inflation rate that it will "target" (i.e. attempt to achieve) in the near to medium term through its monetary policy. The bank will typically attempt to reach this rate of inflation by adjusting interest rates. For example if the current inflation rate is below the target, it will lower rates or hold them low, whereas if the targeted rate is below the current rate, it might raise interest rates (interest rates and inflation rates typically move inversely to each other).
The primary benefit of inflation targeting is reducing uncertainty. Financial markets usually attempt to price in risk, and thus abhor uncertainty, so inflation rate targeting can help alleviate bouts of market volatility. Greater transparency also allows businesses to plan large or long-term investments with more certainty.
The downside with explicit inflation rate targets is that they may curtail the freedom of central banks to respond to crises, leading to larger market gyrations when banks are forced to raise or lower interest rates unexpectedly, since the lack of a rate change may have been "priced in" due to the explicit, publicly announced target that has not been met.