In forex, currencies are always traded in pairs. The first currency is called the base currency and the second currency is called the quote currency. For example, EURUSD, means that the base currency is the Euro and the quote currency is the US Dollar. The quote currency is also referred to as the counter currency.
The ideal way to comprehend base and quote currencies is in terms of exchange rates. An exchange rate of 1.12160, for example, would mean that 1 unit of base currency would cost 1.12160 units of quote currency. So in this case, to own 1 EUR the equivalent of 1.12160 USD is needed, meaning the first currency in a pair is quoted against the second currency.