It differed in a lot of ways from a modern day republic. Venice, Florence or Siena were at their hearth self governing states based on census. In Florence, for example, one had to be a member of the Arti (guilds) to be able to participate in the political arena, and therefore many people were left out, mostly unskilled workers, a few professions which were not recognised and represented by a guild, women, and depending on the period we are talking about nobility. In Venice representation in the Maggior Consiglio was open only to a number of noble families listed in the Golden Book (around 200) and membership was hereditary. Bear in mind, though, that nobility in Venice had a different meaning in comparison with the mainland, as the noble families of Venice acquired their status not through feudal relationships to a monarch, but because of their professional success and wealth (most were merchants, traders, manufacturers). In fact, Venetian nobles did not boast titles such as counts, dukes, etc, but the title of Nobil Homo, or Patrician.

I would say that the Italian republics were more of a plutocracy than a modern day democracy, but considering that European states granted universal suffrage only in the late 1800s and early 1900s, they were pretty evolved IMHO.

One should be aware that in modern political science, a republic simply means a nation who doesn't have a monarch at its head. France is a republic and the USA is a republic, Iraq under Saddam Hussein was a republic, but their systems of government varied greatly. France and USA are democracies, but so ARE UK and Sweden, both of which are also monarchies. So the term "republic" does not in itself imply any particular system of government.