The carry trade is pretty straightforward: it’s a bet that a currency will do certain things in the future and that, given that given-ness, one can use a position on that currency as a hedge, or reduction of risk, on other investments.
In this crisis, many people looked to the way the US was spending money to get out of trouble and assumed that the dollar would stay weak relative to the euro. There is a massive carry trade in the dollar, with the expectation that it stays weak.
With the recent turmoil over Greece, Spain, Portugal, Italy, and Ireland, it looks like the euro may weaken and the dollar strengthen. That will mess up everyone that expected the dollar to stay weak. When it strengthens, the people that had bet on a weak dollar will lose quite a bit of money.