You can read 100 different articles about florence, and chances are that they will have the same or similar point, while using meticulous wording to try and get their point across. But unfortunately for readers, but fortunate for younger (and even older) people who go, you need to know that past the curves of David's huge strap and Giotto's masterpieces, there exists the perfect storm of partying and
positive attitude.
It's not down to the quality of the clubs or the chianti and the San giovese, but the way the city is constructed and its seemingly most popular current use: a "college town".
When Florence/firenze/flotown/f-town was constructed, it was done with no particular order, aside from having several of the most beautiful Cathedrals in the world at its center. There's no grid, and everything can suddenly turn into a maze, or a back alley for a secret bakery or a hot club/bar. Florence is truly a labyrinth.
So aside from the close proximity, as everything is in walking distance, her college atmosphere would not make it anything special. But when students come here for college, it's not school, it's a vacation, usually entirely paid for by their parents. Oh, and 85–90% are girls. So add free liquor, the first time you are out of the country, being a guy/girl in a city filled with others, close proximity of beautiful bars, and needing to meet new people, and it's the perfect storm for a party. Every night.
Example: take a bottle of wine at 7:15 up to piazza michaelangelo. Bring cups. Don't be an asshole. Don't be shy, but don't be like the locals who basically jerk their dicks in front of the students... I guess they've never gotten any.
Now that you spent about $8 on a bottle of chianti and brought your friend, just chill out on the steps, and let the atmosphere of the city bring you to your next group of friends that you don't know yet, and your plans for the night. You'll be overlooking the city at the sunset now, and you're feeling a little tipsy. The girls (or guys) you are with now want to keep it going. After all this is a 4 month vacation, and if you make the most of it, you'll find the essence of the city, some good friends, and awesome nights. Fortune favors the brave.