The European Central bank (ECB) was started in 1998 and, like all central banks, exists to control monetary policy over a given area, in this case, the Eurozone.
The ECB's main function is to keep the price level down. The inflation target for the Eurozone is 2%, and the current rate of inflation in the euro area is 2.7% (March 2011). This suggests that the price level is too high, and trends have shown that it is only increasing. This means that the ECB is expected to use its control over monetary policy to stem this rising interest rate, which it is clearly doing, as on the 7th of April the ECB announced that it would increase euro-area interest rates to 1.25% from 1%.
As well as controlling interest rates, another part of monetary policy is the amount of money printed and injected into the economy as quantitative easing. This can be used to boost AD, but can come at the cost of high levels of inflation, as it involves increasing the supply of money, which will reduce its value.
It has been said, and can be found in the introduction of the stimulus that low base interest rates set by the ECB coupled with high inflation rates in Ireland, Spain and Greece led to negative real interest rates, which put huge amounts of pressure on the banking sector and resulted in very high levels of borrowing and low levels of saving (as money was de-valuing). This is an example of one of the difficulties faced by the ECB, as it has to try and set one set of monetary policies that appeals to everyone. Critics of the system may say that it shouldn't be difficult, as by now the economic cycles of the Eurozone countries should have converged, but clearly they have not, and, as the stimulus mentions, there is risk of a "two-speed" euro area developing.