Again, both statements are true enough if you put them in context. The apparent contradiction comes because just as a given trading center is open for eight hours and yet you can trade 24 hours a day, so it is also true that although any given trading center keeps a five day week, somewhere in the world, another trading center is open when that trading center is closed. It is the happy consequence of the way the day of the week shifts forward or back as you cross the international dateline. 
Each currency pair can be thought of a single unit consisting of a “base currency” (the first currency) and a “counter (or quoted) currency” (the second currency) which can be bought or sold. It shows how much of the counter currency is needed to buy one unit of the base currency. So, in the EUR/USD currency pair EUR is the base currency and USD is the counter currency. If you expect the price of Euro to increase against the price of the U.S. dollar you can buy the EUR/USD currency pair. While buying a currency pair (going long) the base currency (EUR) is being bought, whereas the counter currency (USD) is being sold. Thus, you buy the EUR/USD currency pair at a lower price to later sell it at a higher price and as a result make a profit. If you expect the opposite situation, you can sell the currency pair (go short), meaning sell Euro and buy the U.S. dollar.
Investment management firms (who typically manage large accounts on behalf of customers such as pension funds and endowments) use the foreign exchange market to facilitate transactions in foreign securities. For example, an investment manager bearing an international equity portfolio needs to purchase and sell several pairs of foreign currencies to pay for foreign securities purchases.
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.