Each currency can only be priced in terms of its value against another currency. The price of currency A when paired with currency B (quoted as the A/B exchange rate) can be thought of as "the price of currency A when quoted in terms of currency B."
For example, if the EUR/USD is quoted at 1.3510 then one Euro is priced at 1.3510 US Dollars.
To better understand this concept, think of a stock that's listed on the New York Stock Exchange which would naturally be quoted in terms of US Dollars. Think of the price of General Electric (NYSE symbol: GE) as "GE/USD". If GE is quoted at 30.25, then it's priced at 30.25 US Dollars.