This is a typical "bar" where you can pop in to get your morning coffee. Or hot chocolate con panna (with cream) if you prefer. They have all manner of pastries, cookies and the like to complete your breakfast. Locals frequent this place along with tourists.
Place your order with one of the charming countermen, and either enjoy your coffee the Italian way (standing at the bar) or pay the extra $1 to sit down at a table, inside or out. After you finish, pay at the counter. At lunchtime, you can get pizza by the slice, sandwiches, etc. I recommend the pollo e patate arrosto (roasted chicken and potatoes). This type bar is the most common equivalent of "fast food" in Italy. They also sell gum, bottled drinks, and snacks.
Bars like this are found EVERYWHERE in Florence, and it's fun to find one you like and pop in once a day for a coffee or snack. I recommend this one because all the staff is very friendly, service is quick and the coffee is great. Across the Ponte Vecchio, turn right and go about 3/4 block. There is also an internet access place right across the street to check your e-mail.