There are two key points brought up in book 2. One is the idea that justice/living a just life is better in every way than injustice/ living an unjust life. The second is the theoretical construction of the perfect city (also called the kallipolis), and the rules that govern it.
One of the points Plato emphasizes is the concept of justice having inherent worth. He claims that one should not do the right thing for external reasons (such as rewards of power, money, fame or social acceptance). One should do the right things simply because it is right and should need no other motivation. The purpose of humanity is to enact justice; just as it is the state’s purpose to embody justice.
Plato then begins to talk of the ideal city. He claims that, in order for this city to be perfect, everyone must specialize in a specific task or craft. An individual in this city would do the work he or she is the most suited to/ the best at, and continue to do that task for the rest of their lives. In order to prevent any conflict (from external forces or forces within the city), guardian soldier-police would be instated. These soldier-police would be raised with a strong sense of justice so as not to abuse their power and authority. Their education would help shape this sense of justice and devotion to the city. For instance, they would not be allowed to hear stories or poems in which the gods deceive mortals/ each other or in any other way act unjustly, as it could make them eschew the moral code taught to them.
The city he describes seems, to me at least, to be very controlling and heavy on censorship. It makes me wonder if such a city were to exist how many people would actually want to live there.