The definition of an Indian summer is a period of mild sunny weather that is out of season. The term is commonly used to describe a sunny spell which can occur after the first frost. The first recorded usage of the term was in 1778, from a Frenchman who lived in America called John de Crevecoeur who mentioned it in a letter. The term had spread to Britain by the 19th Century.
Indian summers are caused by stalled high pressure, this high pressure pushes air towards areas of low pressure which makes wind. Due to the rotation of the Earth these winds rotate counter-clockwise about the northern hemisphere and can sometimes curve south picking up warmer air and bringing it further north making it unseasonably warm.