I was taught that the position of the earth relative to the sun marked the change in seasons. Thus, fall starts on the autumnal equinox (on or around the 21st of September) and ends at the winter solstice (on or around the 21st of December). In recent decades, however, I've noticed that more and more people tie the seasons to whole months. Thus, fall starts today, September 1st, and ends on November 30. Winter begins on December 1st, and so on.
Another view of the Saturday market in Sarlat.
The seasons change as the earth's tilt moves toward and away from the sun. The equinoxes occur when the sun is tilted neither toward nor away from the sun. It's the astronomic definition of the seasons, tied to a natural cosmic cycle. The calendar-based meteorological definition seems more or less arbitrary to me, although I've read that it is tied to the earth's average temperature cycle. It looks to me, however, that it's tied simply to the calendar.
So, if you go by the meteorological definition of the seasons, happy fall! If you follow the astronomic definition, you've still got three more weeks of summer ahead.