A carry trade is when you borrow from a currency with a low interest rate, and then invest in a currency with a higher interest rate. Say the US interest rate is 3%, and the Chinese interest rate is 5%. Borrow at 3%, invest at 5%, make 2%, because the Chinese yuan is pegged to the dollar at a fixed rate. Easy! Unfortunately, there's a Peso Problem in this trade, because at any time the Chinese currency could be devalued relative to the dollar, and you can lose years of money in one day.
This trade is really just taking advantage of 'uncovered interest rate parity', where theoretically the differential in currency interest rates should be offset by the expected change in currency rate, plus some risk premium. On average, however, high interest rate countries tend to have currencies that also increase in value. The carry trade blew up in the latter half of 2008, but nicely rebounded, and if you look at over the past 30 years, it remains an 'anomaly' to standard risk models.
The chairman of the China Banking Regulatory Commission complained to Obama that the carry trade was destabilizing the Chinese economy, but this really means the capital inflows are making it hard to keep the currency peg at its low current level. China has a higher interest rate than the US, and though the US dollar is falling worldwide, the yuan remains at its old peg against the greenback. China could float it, and let the market decide, but like most politicians, he does not trust the market. More importantly, there are worried it will hurt exports because a stronger yuan would increase the price of their exports to the rest of the world.
If you meddle with major market prices, like a currency, you invariably make it too high or too low. Finding the 'right' price, is like finding the 'just' price, a subject of endless, fruitless debate. But if the Chinese want to sell us goods at below-market prices all I can say is: thanks for the subsidy!