What does Plato mean (in The Republic) when he identifies that moderation (in
Plato has a number of things to say about moderation in the Republic, but I think the most important one is where he associates moderation with the proper functioning of the appetitive part of the soul. The good news about that part is that it is responsible for the basic functions that keep us alive, such as eating and drinking, and also make us inclined to reproduce. The bad news is that the appetites have a tendency to excess, which--if not prevented by the ruling part of the soul (the reasoning part)--will lead us to do things that are not all things considered really good for us. Hence, moderation in a person will be the result of the "agreement" on the part of the appetitive part to the rule of the reasoning part. The same goes in a city: left to themselves, the craftsmen will have a tendency to excess and dissolution, but when ruled by Plato's philosopher-rulers, the proper functioning of this "appetitive" class of people will allow the whole state to become moderate. Unless and until they agree to allow the best rulers actually to rule, there will always be a high degree of risk that the state will slide into immoderation.
I hope this helps!