Brief description: The J curve shows the possible effects of a devaluation on the balance of payments. If the Marshall-Lerner condition is true then the balance of payments may intially deteriorate and then improve later.
Detailed description: The Marshall-Lerner condition says that if the sum of the price elasticities of demand for imports and exports is greater than 1 then the balance of payments will improve following a devaluation. It is thought that the Marshall-Lerner condition will not be true in the short runbut may be true in the long run. It is this that gives rise to the J curve.