The centrally located Mercato Centrale (repetition intended) is the most popular market in Florence, a gathering place for morning produce grocers, day long food stalls, and the wandering throng of tourists. Locals will tell you that if you're truly into getting an authentic market experience, then avoid the Mercato Centrale and head to the Sant'Ambrogio market, which is open daily until 2pm. Then again, it is close to the sights of city center (the Duomo, the Galleria dell' Academia, etc.) and is sufficiently cheap for produce and on-the-go eating. Try Nerbone if you want delicious sandwiches or pasta, while a number of other stalls are known for seafood, dried fruits, and much more.
Whether you're in town for a while and are gathering meats, cheese, and produce for meals or are in need of your Florence souvenirs, the Mercato Centrale has got it.