Historically, different international monetary systems have emphasized different policy mixes. For instance, the Bretton Woods system emphasized the first two at the expense of free capital movement. The collapse of the system destroyed the stability and predictability of the currency markets. The resultant large fluctuations meant a rise in exchange rate risk (as well as in profit opportunities). Governments now face numerous challenges that are often captured under the term globalization or capital mobility: the move to floating exchange rates, the political liberalization of capital controls, and technological and financial innovation.
Currency carry trade refers to the act of borrowing one currency that has a low interest rate in order to purchase another with a higher interest rate. A large difference in rates can be highly profitable for the trader, especially if high leverage is used. However, with all levered investments this is a double edged sword, and large exchange rate price fluctuations can suddenly swing trades into huge losses.
Once Nixon abolished the gold standard, the dollar's value quickly plummeted. The dollar index was established to give companies the ability to hedge this risk. Someone created the U.S. Dollar Index to give them a tradeable platform. Soon, banks, hedge funds, and some speculative traders entered the market. They were more interested in chasing profit than in hedging risks. 
Traders at the banks would collaborate in online chat rooms. One trader would agree to build a huge position in a currency, then unload it at 4 p.m. London Time each day. That's when the WM/Reuters fix price is set. That price is based on all the trades taking place in one minute. By selling a currency during that minute, the trader could lower the fix price. That's the price used to calculate benchmarks in mutual funds. Traders at the other banks would also profit because they knew what the fix price would be.
The foreign exchange market is the "place" where currencies are traded. Currencies are important to most people around the world, whether they realize it or not, because currencies need to be exchanged in order to conduct foreign trade and business. If you are living in the U.S. and want to buy cheese from France, either you or the company that you buy the cheese from has to pay the French for the cheese in euros (EUR). This means that the U.S. importer would have to exchange the equivalent value of U.S. dollars (USD) into euros. The same goes for traveling. A French tourist in Egypt can't pay in euros to see the pyramids because it's not the locally accepted currency. As such, the tourist has to exchange the euros for the local currency, in this case the Egyptian pound, at the current exchange rate.