The currency exchange rate between two currencies, both of which are not the official currencies of the country in which the exchange rate quote is given in. This phrase is also sometimes used to refer to currency quotes which do not involve the U.S. dollar, regardless of which country the quote is provided in.
For example, if an exchange rate between the British pound and the Japanese yen was quoted in an American newspaper, this would be considered a cross rate in this context, because neither the pound or the yen is the standard currency of the U.S. However, if the exchange rate between the pound and the U.S. dollar were quoted in that same newspaper, it would not be considered a cross rate because the quote involves the U.S. official currency.