The original nation must have lived in Central Asia in the fourth millennium BCE, and moved to the south at the end of the third or the beginning of the second millennium. In what is now Uzbekistan, they appear to have separated into two groups, one of them invading the Punjab and the other Iran. Perhaps, the division was caused by a religious dispute, because the words for "demon" and "deity" are linguistically related but theologically opposite (Indian: asura and deva; Persian: daiva and ahura).
As said, the expression is used in many ancient Iranian sources. For instance, when king Darius I the Great (522-486 BCE) ordered new, Persian alphabet to be developed, he called it an "Aryan script". The Sasanians created the political concept of Iran (Eranšahr) as a unity of Aryan nations; Eran and Aneran were often contrasted, the former referring to the Sasanian Empire, the latter to, e.g., the Roman Empire or the tribal areas in the northeast.
The expression has been abused by the Nazis (who contrasted the Aryans to the Semites). For obvious reasons, modern linguists now prefer "Indo-Iranian". However, in countries like modern Iran, the old expression is still used.