I don't think it's easy to describe in words. You actually have to be there. I've lived in a suburb of Toronto for most of my life (similar to a random American suburb), and when I went to Florence for the first time, I had a sense that the city was alive, independent of the people in it. It felt as if I was a part of something, even though I was just visiting for a couple of weeks. On the other hand, I didn't feel that in Rome.