~Some Interpretations~
The society Socrates was trying to describe in his City in Speech was that of a communist society. Although there was to be class distinctions in this city, the chances a person (or baby, rather) had of becoming a member of a certain class were no greater than those of the next person.

Everything amongst the classes was equal. In addition, there was a certain equality woven throughout the entire city. Every citizen went through the same education and was taught the same virtues. In fact, the same parents raised everyone since the the community brought up all the children together.

The Guardians dictated everything about the life of everyone. There was no climbing the social ladder and working your way up to the top class or becoming the best anything you could be. You were what you were determined to be at birth, and there was no improving or changing it. Change was frowned upon. The most important thing was the city as a whole: to make sure the city was a happy one, that whatever was done was done in the best interest of the city, and that, most importantly, the city came first. In these ways and many more, the society of the City in Speech had a certain communist-like atmosphere and way about it.

Please refer to Major Concepts of Book IV for a more in depth look at the City in Speech and the Four Virtues.