This tradition is very ancient and is connected the Feast of the Nativity of the Virgin Mary (especially its eve, the evening of September 7th). Throughout the town you'll see parades of adults and children holding their Rificolone (paper lanterns, hanging from a long stick). The events will culminate in Piazza Santissima Annunziata.
There are interesting exhibitions at Casa Buonarroti in Florence during the summer. The first of these is particularly fascinating and is dedicated entirely to the figure of Matilda of Tuscany or of Canossa, the powerful and well-respected countess who spent 14 years of her life in Florence.