The Church's liturgical calendar only has three birthday celebrations: for John the Baptist, Mary, and of course Jesus. This departure from the Church's usual custom of celebrating a saint's birth into eternal life can tell us something about Mary. Her whole life was significant in God's plan of salvation. So we can rejoice in the birth of this baby girl who was to play such an important role for us.
The book At Worship with Mary by Christopher O'Donnell, O. Carm., has some other information about this feast. It was probably first celebrated in Jerusalem around the 5th century. Why in September? Of course we don't know the actual date of Mary's birthday. But in Constantinople, as in all the East, the year began on September 1. The 8th was chosen (I'm not sure why that particular day). The date of this feast determined the date of the feast of Mary's Immaculate Conception--December 8, going 9 months backward.
With Mary's feast came the dawn of our salvation.