During the 15th century, the Medici family were required to open banks at foreign locations in order to exchange currencies to act on behalf of textile merchants. To facilitate trade, the bank created the nostro (from Italian, this translates to "ours") account book which contained two columned entries showing amounts of foreign and local currencies; information pertaining to the keeping of an account with a foreign bank. During the 17th (or 18th) century, Amsterdam maintained an active Forex market. In 1704, foreign exchange took place between agents acting in the interests of the Kingdom of England and the County of Holland.
The world then decided to have fixed exchange rates that resulted in the U.S. dollar being the primary reserve currency and that it would be the only currency backed by gold, this is known as the ‘Bretton Woods System’ and it happened in 1944 (I know you super excited to know that). In 1971 the U.S. declared that it would no longer exchange gold for U.S. dollars that were held in foreign reserves, this marked the end of the Bretton Woods System.
The foreign exchange market is 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.