The order of events is the whole point. Autumn has already started. The leaves have turned, people have their jackets on, and then the warmth comes back for a short while, as if summer had forgotten to leave. That late return is what the phrase names. It normally takes an: we had an Indian summer. The I is capital. One thing to know about the name: some speakers feel the Indian in it is a problem and say a late warm spell instead, though the phrase is still common in news and everyday talk. Where it started is not settled; several explanations are offered and none is proved.

This use moves the weather picture onto a life. A life or a career has seasons too: youth as summer, old age as winter. An Indian summer is the bright warm spell that turns up just before the winter. So it names late success. Someone may do their best work after they retire. An older player may suddenly be brilliant again in a last season. The feeling it carries is warm rather than sad, though the coming winter is quietly part of the picture. A common shape is the Indian summer of his career.