From AMS Glossary
A period, in mid- or late autumn, of abnormally warm weather, generally clear skies, sunny but hazy days, and cool nights.
In New England, at least one killing frost and preferably a substantial period of normally cool weather must precede this warm spell in order for it to be considered a true "Indian summer." It does not occur every year, and in some years there may be two or three Indian summers. The term is most often heard in the northeastern United States, but its usage extends throughout English- speaking countries. It dates back at least to 1778, but its origin is not certain; the most probable suggestions relate it to the way that the American Indians availed themselves of this extra opportunity to increase their winter stores. The comparable period in Europe is termed the Old Wives' summer, and, poetically, may be referred to as halcyon days. In England, dependent upon dates of occurrence, such a period may be called St. Martin's summer, St. Luke's summer, and formerly All-hallown summer.