Idioglossia refers to an idiosyncratic language, one invented and spoken by only one or a very few people. Most often, idioglossia refers to the private languages of young children, especially twins. It is also known as cryptophasia, and commonly referred to as twin talk or twin speech.
Children who are exposed to multiple languages from birth are also inclined to create idioglossias, but these languages usually disappear at a relatively early age, giving way to use of one or both of the languages introduced.
Kennedy twins of San Diego, California, who were subjected to intensive study, including an exhaustive analysis of their language. (they named themselves "Poto and Cabengo")
Media
The 1994 film Nell, starring Jodie Foster, depicts a woman who speaks an idioglossia. The stage play on which it is based is also called Idioglossia.