@winterflags above has some of the main ideas. Also:
A) Although compared with a year or two ago, the GDP per capita doesn't look low, if you compare it with the value if it had continued the trend it had before 2008, then it looks low, particularly in southern Europe. Also, they don't look so much at GDP per capita, but at the 'slack' in the economy which they measure with some measure of unemployment. Unemployment is positively enormous in Spain, Greece, Portugal, etc.
B) Inflation is very low in Japan and Europe, and economic growth is very low in both. Moreover, inflation has stayed low in Japan despite its ever-looser monetary policy, so they want to do something extreme to see if that brings about some inflation!
C) Inflation at or below 2% looked like a reasonable target before the crisis. However, now that we know that big recessions are still possible, it seems necessary to keep inflation at 2% or a bit higher. This seems a good idea because when inflation is higher, then it's easier to create large negative real rates by setting nominal rates to zero.
D) It seems also that they want to make sure that banks don't have a liquidity problem. During the financial crisis, there seemed to be times when liquidity was in high demand. Treasury bonds paid negative interest rates for a period. One way to interpret this is that the market has a high demand for safe assets and so the central banks, by buying bonds with reserves, increase the supply of very safe assets, ie. reserves. Potentially they also create a 'search for yield' phenomenon, which can create bubbles, but that's another matter.
E) The last reason is that probably because of particularly dogmatic, nearsighted politics both in the US and European Union, both economies failed to engage in strong expansionary fiscal policies. They did increase fiscal deficits, but not too much. The crisis was thus not resolved and their debt burdens increased anyway, they increased a lot through the accumulation of many not-so-large deficits! A few years later, we still have sort of a crisis, but we have very little fiscal 'margin': most large countries have a lot of debt relative to historical norms. Therefore the only policy available seems to be monetary policy, so central bankers keep pushing and pushing rates down. People call it "pushing on a string" at this point, but its still seems politically impossible, in Europe at least, to increase spending.