I'm talking about its development post-Carolingians and I suppose after its independence from the Holy Roman Empire.
I got into a ^(well ^meaning) argument about this with the other Italian medievalist on this sub a few months back, you can read the whole thing here.
All the comments and all the back and forth is really in-depth and gives a good overview of high medieval Italian history (I still maintain that the other poster is confusing Ostrogothic social structure with Longobard social structure, but let's not go into that).
To be brief, I would tell you that Italy was indeed a unified kingdom for over two hundred years (more or less continuously) after the fall of the roman empire. However, after the early breakdown of the feudal system (why? Read this), the population density of in Northern Italy, coupled with the power vauum after the Carolingian conquest and facilitated by holdovers of the preexisting social structure ^including ^bishops preserved by the Ostrogoths and Lombards facilitated the development of cities, often governed as (very limited) republics. As some of these republics grew in power and wealth, they subjugated their neighbors, and came to rule over large areas. As their wealth increased further, often one political faction or family came to dominate the rest, and the republic was toppled in favor of a monarchy.
Every Italian State had its own unique story, with individual cities, factions, artists, rulers, and political idiosyncrasies. Each Italian state came to be thanks to a very specific set of circumstances. I have tried to give you a generic overview. If you're very interested, I would suggest reading A History of Venice by good old J. J. Norwich. Even though the Republic of Venice is, of course, a unique case among the Italian states (not only did its republican government resist being toppled in favor of a monarchy, was the most powerful Italian state to the end) through its history the Republic has interacted with the Carrara, rulers of Padua, the Della Scala of Verona, and, of course, the Visconti of Milan; its history is a great starting point to dive into Italian history.
What time period are you talking about?