If you are travelling to Florence for a city break in order to see the main sights, and soak up the atmosphere, then the best time to visit is between May and June, or during September and October, when the weather is pleasantly warm, and the crowds in the city are not quite so vast. High summer sees Florence become sticky, when the narrow streets trap the heat, and walking around in large crowds is an unpleasant experience.
If on the other hand, you are spending a longer holiday exploring Tuscany as a whole, and not just staying in the city, then the hot summer weather is great for walking in the countryside and seeing the smaller villages there.
Winter in Florence sees the hotel rates go down, and the weather is cool, although still warm enough for walking around making Florence a good choice at almost any time of the year.