In a currency pair, the first currency in the pair is called base currency and second is called the quote currency.
Currency pairs can be divided into two types, direct and indirect. In a direct quote, the Domestic Currency is the base currency and the foreign currency is the quote Currency. An indirect Quotation is just the opposite: foreign currency is the base currency and the national currency is the quote Currency. For an American trader, in the quote EUR/USD is indirect. For example, a Quote Of 0.80 EUR/USD means that 1 Euro will cost you 0.80 USD.
Although almost 89% of foreign exchange transactions worldwide involve the US dollar, the currency pair EUR/USD is always indirectly. The reason for this is mostly Convention. The pair EUR/USD can easily be shown in the USD/EUR by making a simple calculation, but there are no strict rules that determine whether a currency pair is manifested directly or indirectly. By the way currency pairs are quoted can also vary depending on the country in which the trader lives in most countries use direct quotes, and in the UK, Australia, New Zealand and Canada prefer indirect quotes.
For further reading on currencies Forex see: 6 factors that influence exchange rate , the Top 6 questions about currency trading and the Currency cross your boss.