The foreign exchange market (also called forex) is a trading market where individuals, 
companies, and governments exchange different currencies. The general purpose of the forex market is to assist and facilitate international trade by establishing a market where one currency can be bought by selling another. This allows companies and other entities that do business in foreign markets to accept local currency and transfer it back to the home currency of the firm.
In a foreign currency exchange, the two currencies that are being traded are called currency pairs. Each currency pair has its own market based on supply and demand fundamentals for the pair. There are literally hundreds of different currency pairs due to the fact that nearly every sovereign nation has its own currency. The big exception is much of Europe, which has a common currency.
While some trades occur in the smaller currencies, the vast majority of trades occur in seven well known currencies. These currencies belong to the largest, most stable economies whose governments do not fix their currencies or unduly manipulate their exchange rates. The United States Dollar (USD) is by far the heaviest traded, being part of over 75% of all currency trades. Next most prevalent is the Euro (EUR), the common market currency for much of Europe. Also heavily traded are the Japanese Yen (JPY), British Pound Sterling (GBP), the Australian Dollar (AUD), the Swiss Franc (CHF) and the Canadian Dollar (CAD).
The currency prices are quoted by their currency pairs. An example is EUR/USD, which is the Euro and the US Dollar. The first currency listed in the pair (EUR) is the base currency and the second (USD) is the quote currency. For example, if this currency pair had a price quote of 1.3763, it means that for every 1 Euro you could exchange it for 1.3763 US Dollars. It is important when receiving a price quote to understand the currency pairs and to know the order of each of the currency in the pair. In general, the order of the pair is standardized so the USD will nearly always be the quote currency in the EUR/USD pair.
The most common trade in the foreign exchange market is between the Euro and the US Dollar (EUR/USD), followed by the US Dollar and Yen (USD/JPY) and the Pound Sterling and US Dollar (GBP/USD). The rest of the major currency pairs consist of the rest of the commonly traded currencies paired with each other.