We are in the middle of a pretty bad recession, and the federal government lead by Obama want to increase government spending on incredible levels. How this is supposedly supposed to pull us out of a recession is still a mystery
Because the recession is resulting from reduced demand; people cut back on their spending, causing businesses to fail (especially since finance has dried up meaning they can't obtain a loan to keep them going until spending picks up again), causing increased unemployment+job uncertainty, causing people to cut back on their spending, and so it goes on.
The capacity is there in the economy to obtain a higher output, hence if people aren't going to increase their spending to utilise this, the government can look to increase demand to expand the economy to this point (or at least closer to it than if they did nothing). The end result of this (if it goes to plan of course) is that you can avoid the worse parts of a recession, and then when the economy is back on track and starting to grow again the government help can be withdrawn. The economy will get to that position eventually, but the idea of increased government spending is to get us there sooner ("in the long run we are all dead").
Of course it helps if you are starting from a fairly strong (budgetary) position which will allow you to borrow enough in the short term to have the desired effect. Also working out the amount required for the desired effect, and how best to target, are also far from clear. One option the government has would be to cut taxes. However for many people in these uncertain times they would likely keep much of the surplus rather than spend it. So another alternative is for the government to give handouts to people on lower incomes. They're much more likely to spend it (due to their lower incomes), and so that is another option. There are of course plenty of other ways, but that gives a basic introduction to it.
The more long term idea behind this would be to smooth out output growth so that it is stable and positive - the government should save a bit in the good years, and then when the economy looks to be headed to a recession use those savings to keep it growing (or at the very least not shrinking). The economy benefits even more in this situation from avoiding the negative effects of the recession, and providing greater confidence in the economy allowing businesses to plan and invest with greater confidence. A shame then that a republican president has been responsible for running up hefty deficits during the 'boom' years.
