Managed (or dirty) floating refers to a system whereby exchange rates are allowed to float, but from time to time the authorities will intervene in the foreign exchange market:

To use their official reserves of foreign currencies to buy their own domestic currency

To sell their domestic currency to buy more foreign currency for the official reserves

In practice, many governments seek to combine the advantages of exchange rate stability with flexibility and avoid the disadvantages of both rigidly fixed exchange rates and free-floating.