When you trade in the Forex Market, you will trade "Currency Pairs". This is the source of a lot of initial confusion for new traders. "Why Pairs? Why can't I just trade Dollars, or Euros or Francs?" is a question you hear often. The answer is easy, every exchange on the Forex Market (or at any border exchange kiosk for that matter) involves two different currencies. You are trading US Dollars for Canadian Dollars, British Pounds for Euros, Euros for Japanese Yen, Australian Dollars for Mexican Pesos or one country's currency for another's. This exchange is done on the Forex Market by trading currency pairs. For instance, when you are trading the EUR/USD pair, you are exchanging Euros and US Dollars. If you believe that the Euro is going to strengthen against the US Dollar, you buy the pair. If you believe that the US Dollar is going to strengthen against the Euro, you sell the pair.
In each pair, the first pair is the primary currency, or the currency against which the other is denominated. This means that in any quote for the EUR/USD, the EUR number is always 1. So if the quote for the EUR/USD is 1.3547, that means that it takes 1.3547 US Dollars to purchase 1 Euro. If you are following the USD/JPY and the quote is 112.58, that means that it takes 112.58 Japanese Yen to purchase 1 US Dollar. For the GBP/CHF, if the quote is 1.5128, it takes 1.5128 Swiss Francs to purchase on British Pound. You get the idea.
When you are "buying the pair" you are, in effect, borrowing the second currency to buy the first. So, if you are buying one standard lot of the EUR/USD, and the quote is 1.3547, you are borrowing USD $135,470 in order to purchase €100,000. Your hope is that the Euro will strengthen and you will sell your Euros and get more US Dollars for them. For example, if the pair rises to 1.3850 and you sell your position, you will get USD $138,500 for the €100,000 you bought. After repaying the loan of USD $135,470, you will net USD $3,030, which is your profit for the trade. To give an example of how the other side would work, if you think that the Australian Dollar is going to weaken against the Japanese Yen, then you would sell the AUD/JPY pair. Suppose that the quote for the pair was 71.60 (meaning that 1 Australian Dollar cost 71.60 Japanese Yen), you would borrow 100,000 worth of Australian Dollars and purchase ¥71,600,000. If the AUD did weaken and the price for the pair fell to 69.90, you would sell your Yen and pay off the loan to your broker and have ¥1,700,000 in profit, which would be converted to whatever currency you trade in and credited to your account (in US Dollars you might get $17,000, in Euros you might get €13,000).
I hope that helps clear up some confusion on why currency is traded in pairs. As always - Happy Trading!