An exonym is a name used to refer to a place or people, by people outside the location or group instead of the name used by those who live there. Good examples are Japan which is referred to in Japanese as Nihon or Nippon, or Germany, locally known as Deutschland. "Exonym" comes from Greek roots "ex-" (out) and "-onym" (word, name). Sometimes exonyms come from older names of the region/people in question, or alterations of the local name to fit the phonetic patterns of a different language. Other times, the name of a people for their neighbors becomes the name that is widely used (such as the ancient Mesopotamian nation known as Sumer, which was so called by the nearby Akkadians. The Sumerian name for themselves was "Kanga" or "Kienga").

When doing research, exonyms can cause problems. If you search online or look in indexes for an exonym, the results will be biased toward the views of people who use that particular name, or the time when that exonym was in wide use, and local or current views can be left out. The use of an exonym in speech can mark the user as an outsider or even make them seem prejudiced against the locals; one site referred to them as possible markers of linguistic chauvinism.

Sources:
http://wordsmith.org/awad/archives/0503
http://www.bartleby.com/61/95/E0279550.html
http://education.yahoo.com/reference/dictionary/entries/95/e0279550.html
http://www.ifag.de/kartographie/Stagn/Exonyme/VorwortENG.htm
http://www.fact-index.com/s/su/sumer.html