Krugman coined the phrase on his blog to describe the British government’s economic policies. I like the term, but in truth, I think all Keynesianism must be of the “crony” variety, in practice if not in theory.
Keynesianism says that in a period of declining aggregate demand, the government must spend money to boost the economy. (That’s the super-simplified version.) Well, if politicians are spending money, you can bet that they will make sure to spend it on their friends and their pet projects. This is still just as stimulative to the economy as any spending, so the Keynesian theory is fulfilled, but at the same time, it’s a kind of corruption.
But, as Krugman says, it’s still a sound economic policy overall. It’s just that politicians take advantage of it to engage in a little cronyism on the side. Only to be expected, because you can’t really be a politician without engaging in cronyism.