Quantitative easing is when a central bank buys tons of financial assets to try to kickstart the economy. Central banks buy and sell government debt—a process called open market operations—to influence how much money there is in the economy. They did a lot of this in 2008, to try and decrease interest rates, and get more investment going. And it worked—sort of. A major problem with using interest rates to stimulate the economy is that it's fairly difficult to reduce them below zero. A negative interest rate basically means that lenders have to pay borrowers—instead of the other way around—which isn’t something economists expect to happen very often.
Quantitative easing, often called QE, is a lot like open market operations, but on a much bigger scale. Instead of just buying small amounts of short term government debt to nudge interest rates down, QE is about buying huge amounts of different financial assets, so that you’re not only putting more money into the economy—you’re also propping up sectors that are on the verge of collapse by buying them out.
QE is quite new, and still fairly experimental. And as you might have guessed, it’s also quite controversial. A lot of economists think it was necessary to keep the crisis from completely wrecking the economy, but some aren’t convinced it did much to help, and are worried that it might cause inflation whenever the economy finally picks back up.
There’s also the question of what central banks were actually buying. When central banks buy government debt they make it easier for governments to run deficits. That can be a good thing for governments, but it could encourage reckless spending by politicians. Similarly, when central banks buy private financial assets, they usually end up helping banks and other financial institutions. There’s now a campaign for something called QE For the People. The basic idea is that instead of creating money to buy financial assets, central banks could invest it directly in public investment projects like building new schools or financing healthcare projects. It’s a pretty exciting idea, but most economists would say it’s also pretty dangerous, as money creation could easily get out of control and lead to inflation.