It is the American version of British All-Hallows summer, French été de la Saint-Martin (feast day Nov. 11), etc. Also colloquial was St. Luke's summer (or little summer), period of warm weather occurring about St. Luke's day (Oct. 18). An older and simpler name for it was autumn-spring (1630s).
"inhabit of India or South Asia; pertaining to India," c. 1300 (noun and adjective), from Late Latin indianus, from India (see India). Applied to the aboriginal native inhabitants of the Americas from at least 1553 as a noun (1610s as an adjective), reflecting Spanish and Portuguese use, on the mistaken notion that America was the eastern end of Asia (it was also used occasionally 18c.-19c. of inhabitants of the Philippines and indigenous peoples of Australia and New Zealand). The Old English adjective was Indisc, and Indish (adj.) was common in 16c.
Red Indian, to distinguish the native Americans from inhabitants of India, is first attested 1831 in British English (Carlyle) but was not commonly used in North America. Hugh Rawson ("Wicked Words") writes that "Indian is unusual among ethnic terms for not having much pejorative value until comparatively recently." A few phrases, most of them U.S., impugn honesty or intelligence, such as Indian gift:
An Indian gift is a proverbial expression, signifying a present for which an equivalent return is expected. [Thomas Hutchinson, "History of Massachusetts Bay," 1765]
Hence Indian giver "one who gives a gift and then asks for it back" (1848). Also compare Indian summer. Indian elephant is from c. 1600; Indian corn is from 1620s; to walk Indian file is from 1758. Indian club is from 1824 as a weapon, 1825 as exercise equipment (clubs were noted in Lewis & Clark, etc., as characteristic weapons of native warriors in the American West). Indian-head (adj.) in reference to U.S. copper pennies with a portrait of an Indian in profile, from 1862.
"hot season of the year," Old English sumor "summer," from Proto-Germanic *sumra- (source also of Old Saxon, Old Norse, Old High German sumar, Old Frisian sumur, Middle Dutch somer, Dutch zomer, German Sommer), from PIE root *sm- "summer" (source also of Sanskrit sama "season, half-year," Avestan hama "in summer," Armenian amarn "summer," Old Irish sam, Old Welsh ham, Welsh haf "summer").
As an adjective from c. 1300. Summer camp as an institution for youth is attested from 1886; summer resort is from 1823; summer school first recorded 1810; theatrical summer stock is attested from 1941 (see stock (n.2)). Old Norse sumarsdag, first day of summer, was the Thursday that fell between April 9 and 15.
type of defensive opening in chess, 1935, in reference to Aron Nimzowitsch (1886-1935), Latvian-born Jewish chess genius who popularized a variation of the Indian defense (1884) attributed to Indian chess player Moheschunder Bannerjee.