In a currency pair quote, the base currency, also known as the primary currency, is the first currency shown. The second currency shown is referred to as the quote currency.
Currencies are quoted in relation to other currencies. For example, in the EUR/USD currency pair, EUR is the first currency shown, and always has a value of one. The base currency is the reference element for the exchange rate of the currency pair.
You may see a quote look something like this: EUR/USD 1.30, which means that the value of one euro is equal to 1.30 dollar.
In foreign exchange markets, normally the most liquid currency is quoted as the base currency. In that sense, the dollar is the base currency in all dollar crosses with four exceptions: against the euro, the pound sterling, the Australian dollar and the New Zealand dollar.