Free floating exchange rates are set purely by market forces , currency appreciates and depreciates with no intervention by the central bank. Therefore currency value isnt a monetary policy target.
Managed floating exchange rates are driven by the market forces, however the central bank may intervene by buying reserves to support a currency and selling to weaken a currency. Currency is a target of domestic monetary policy.
Fixed exchange rates occur when the central bank peggs a currency to another stable currency such as the Euro. The central bank has to hold enough reserves to intervene in currency markets when needed to maintain the fixed currency peg.
Advantages to a free floating market
No central bank intervention means there is no need for high levels of foreign exchange reserves
Marketforces adjust the exchange rate efficiently
Monetarypolicy can be focused on inflation instead of buying reserves
Reduced chance of speculative attacks as currency value is determined by market forces.
Disadvantages of floating exchange rates
Exchange rate volatility may be harmful for foreigndirectinvestment if confidence is lost.
Smaller nations, largely primary sector exporters, may be more vulnerable
Can cause inflation, weak currency - imports more expensive, cost push inflation