A carry trade is borrowing in one currency, that has a lower interest rate, to buy another that has a higher interest rate. The trader expects to be able to make a sufficient profit on the difference in interest rates to more than cover depreciation in the high interest paying currency.
Because the currency that is sold is borrowed, the interest that has to be paid is a holding cost or carrying cost, hence the term carry trade.
For a more detailed discussion see uncovered interest arbitrage.