What are freely floating exchange rates and fixed exchange rates?
Freely floating exchange rates refer to the exchange rates between currencies of different countries where there is no interference of any sort from the government, usually through the central bank, to keep the exchange rate at a level that is fixed by them. If the exchange rate is fixed, the government interferes in the forex market and controls the exchange rate by manipulating demand and supply by either selling from its reserves or buying to add to its reserves.
An example of a floating exchange rate is that between the US dollar and the Euro. This is not controlled in any way. Factors like interest rates, investments, inflation, economic growth rates, perceived risk, etc. determine the exchange rate between the two. It is not controlled in any way by the Federal Reserve selling or buying Euros. On the other hand, the exchange rate between the Chinese Renminbi (Yuan) and the US Dollar is fixed by the Chinese government. Whenever the Yuan depreciates against the dollar, the Chinese Central Bank sells US dollars from its forex reserves in the open market. If there is an appreciation in Yuan this is countered by the Chinese Central Bank buying dollars from the forex market.