Geographical names used in a certain language for

geographical entities situated outside the area
where that language has official status

and

differing in its form from the name used in the offical language of the area where the geographical entity is situated. (2nd UNCSGN1972).

What kind of objects generates exonyms?

• Objects in areas close to linguistic borders,
  
  
• Important objects further from linguistic border (names of countries, capitals, large rivers).

Have a look at Glossary of Terminology (pdf), too!