The carry of an asset is the return obtained from holding it (if positive), or the cost of holding it (if negative) (see also Cost of carry).
For instance, commodities are usually negative carry assets, as they incur storage costs or may suffer from depreciation. (Imagine corn or wheat sitting in a silo somewhere, not being sold or eaten.) But in some circumstances, appropriately hedged commodities can be positive carry assets if the forward/futures market is willing to pay sufficient premium for future delivery.
This can also refer to a trade with more than one leg, where you earn the spread between borrowing a low carry asset and lending a high carry one; such as gold during financial crisis, due to its quality.
Carry trades are not usually arbitrages: pure arbitrages make money no matter what; carry trades make money only if nothing changes against the carry's favor.
For instance, the traditional income stream from commercial banks is to borrow cheap (at the low overnight rate, i.e., the rate at which they pay depositors) and lend expensive (at the long-term rate, which is usually higher than the short-term rate).
This works with an upward-sloping yield curve, but it loses money if the curve becomes inverted. Many investment banks, such as Bear Stearns, have failed because they borrowed cheap short-term money to fund higher interest bearing long-term positions. When the long-term positions default, or the short-term interest rate rises too high (or there are simply no lenders), the bank cannot meet its short-term liabilities and goes under.
The currency carry trade is an uncovered interest arbitrage.
The term carry trade, without further modification, refers to currency carry trade: investors borrow low-yielding currencies and lend (invest in) high-yielding currencies. It is thought to correlate with global financial and exchange rate stability and retracts in use during global liquidity shortages, but the carry trade is often blamed for rapid currency value collapse and appreciation.