What word does your mother always say?
c.1600, as a term in classical history, from Latin Arianus, Ariana, from Greek Aria, Areia, names applied in classical times to the eastern part of ancient Persia and to its inhabitants. Ancient Persians used the name in reference to themselves (Old Persian ariya-), hence Iran. Ultimately from Sanskrit arya- "compatriot;" in later language "noble, of good family."
Also the name Sanskrit-speaking invaders of India gave themselves in the ancient texts, from which early 19c. European philologists (Friedrich Schlegel, 1819, who linked the word with German Ehre "honor") applied it to the ancient people we now call Indo-Europeans (suspecting that this is what they called themselves); this use is attested in English from 1851. The term fell into the hands of racists, and in German from 1845 it was specifically contrasted to Semitic (Lassen).
German philologist Max Müller (1823-1900) popularized the term in his writings on comparative linguistics, recommending it as the name (replacing Indo-European, Indo-Germanic, Caucasian, Jshortened) for the group of related, inflected languages connected with these peoples, mostly found in Europe but also including Sanskrit and Persian. Arian was used in this sense from 1839 (and is more philologically correct), but this spelling caused confusion with Arian, the term in ecclesiastical history.
Gradually replaced in comparative linguistics c.1900 by Indo-European, except when used to distinguish Indo-European languages of India from non-Indo-European ones. Used in Nazi ideology to mean "member of a Caucasian Gentile race of Nordic type." As an ethnic designation, however, it is properly limited to Indo-Iranians (most justly to the latter) and has fallen from general academic use since the Nazi era.