Lingua franca, literally "Frankish language" in Italian, was originally a mixed language consisting largely of Italian plus a vocabulary drawn from Turkish, Persian, French, Greek and Arabic and used for communication throughout the Middle East. The term is now applied to any language used by speakers of different languages to communicate with one another.
See the two sections below for further details of each of these two uses of the term.
In a general sense
The term lingua franca refers generally to a language learned, beyond its native speakers, for international commerce or other extended intercultural interactions. It has acquired this general sense by extension from the specific language described below. The Franks were an ancient Germanic people. The terms Frank and Frankish were used by Arabs for Christians. In the Roman Empire and for the following millenium the lingua franca was Greek in the east and Latin in the west. French language also served as lingua franca later on. French has been the language of diplomacy in Europe from the 17th century, and as a result is still the working language of international institutions and is seen on documents ranging from passports to airmail letters. German served as a lingua franca in portions of Europe during the 19th and 20th centuries, especially in business. English is the current lingua franca of Western international business and is displacing French in diplomacy.
In other regions of the world, other languages perform the function of a lingua franca: Swahili in East Africa, Russian in areas formerly associated with the Soviet Union, Hindi (along with English) in India, Malay in South-East Asia, Bislama in the Pacific Islands, and various Pidgin languages in other locations and times. Portuguese served as lingua franca in Africa and Asia in the 15th and 16th centuries. Mandarin Chinese also serves a function of providing a common spoken language between speakers of different and mutually unintelligible Chinese dialects.
See also: international auxiliary language
In a specific sense
Lingua Franca meaning "Frankish language" was an early language, used in the Mediterranean area from the 14th century or earlier and still in use in the 20th century. Lingua Franca was known by Mediterranean sailors including the Portuguese. When the Portuguese started exploring the seas of Africa, America, Asia and Oceania, they tried to communicate with the natives by mixing a Portuguese-influenced version of Lingua Franca with the local languages. When English or French ships came to compete with the Portuguese, the crew tried to learn this "broken Portuguese". Through a process of change the Lingua Franca and Portuguese wordstock was substituted by the languages of the peoples in contact.
Lingua Franca used to be a publication which was a "great magazine about intellectual and literary life in the academy" according to Dennis Loy Johnson at http://www.mobylives.com/Lingua_Franca_demise.html