The second summer, or the summerly time which sets in about All-Hallows-tide. Called by the French, L'été de St. Martin (from October 9th to November 11th). Also called St. Luke's Summer (St. Luke's Day is October 18th). The Indian summer. Shakespeare uses the term—
“Farewell, thou latter spring; farewell, All-hallown Summer!” 1 Henry IV. i.2.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894