In essence, the myth tells us Socrates’ view of the city and its people.
First of all, the people of the city (humans in general) are shackled in intellectual darkness (Republic, 514). This is understood as meaning that we confuse our material existence, the material world with which we interact, and the way by which we interact with it, as being real and true, when in fact it is best understood as a shadow of what is actually real and true, namely the world of the forms and ultimately the Good itself (515c). Secondly, the vast majority of humans are unconcerned about the falseness of their existence and find anyone suggesting otherwise as ridiculous to the point of perhaps trying to kill them (517a). Third, as a consequence, the vast majority of people in the city do not recognize the Good, and thus do not truly recognize the things derived from the good (e.g., justice).
However, the fact that there are individuals within the City (true philosophers) who try to inform the people regarding the reality of the Good etc., means that there is the possibility of movement between the life of intellectual bondage in darkness and intellectual knowledge in the light. So, fourth, it is necessary for those who are rulers to recognize both the basic deceit which shrouds the majority of the citizens and the need for those who know the reality of the Good to provide leadership and instill justice (etc) in the city by way of its laws and the ordering things in a harmonious way (520). Fifth, this further requires a deliberate approach to education by the founders so that those who are liberated from the cave are further examined to determine their suitability for leadership and instill a sense of obligation to return to the realm of the cave for the good of the city (532ff). Sixth, those who return must be fully aware that the majority of the people in the city are unconcerned about the true reality of the Good, and so they are allowed to continue in deceit (and are in fact further deceived) in order to instill (or perhaps coerce and deceive) and sustain (or perhaps enforce) harmoniousness in the city for all people (519e). Finally, the philosopher-kings, mere philosophers, mere rulers, and founders are to order the procreation of the citizens and their education in such a way to ensure that there will be future philosopher-kings able to lead for a time for the benefit of the city before being relieved to withdraw from sensory and material concerns and to return to pure contemplation of the Good (519c, 540b).