A cross rate is the currency exchange rate between two currencies when neither are the official currencies of the country in which the exchange rate quote is given. Foreign exchange traders often use the term to refer to currency quotes that do not involve the U.S. dollar, regardless of what country the quote is provided in.
Understanding cress rates, is a exchange rate between the euro and the Japanese yen is considered to be a cross rate in the market sense because it does not include the U.S. dollar. In the pure sense of the definition, it is considered a cross rate if it is referenced by a speaker or writer who is not in Japan or one of the countries that uses the euro. While the pure definition of a cross rate requires it be referenced in a place where neither currency is used, the term is primarily used to reference a trade or quote that does not include the U.S. dollar.