Plato was not a democrat. He did not believe that all people are equal or that the people are able to know best how to govern themselves. Instead, his ideal form of government was one in which everyone knew their place in society. It was a government in which the best people ruled while the others obeyed.
Plato says that human society is at its best when people are doing the thing at which they are best. Therefore, a society is at its best when it is ruled by the best people. The best people are those who are naturally fitted to ruling, not those who can gain enough votes to win an election.
In Plato’s idea society, government is run by a class called the guardians. These are philosophers who know what is good and what is bad. Because they know these things, they can set up society in the correct way. They are people who love truth and knowledge above all else and apply what they learn to society. They have to be chosen at a young age and developed so they will be worthy of ruling.
Below them is a group called the auxiliaries. These are people who love honor above everything else. They are brave and patriotic. They defend the state. Finally, there are all the other people. They are called the producers and they are good at making things. They want material comfort and wealth above all else, which makes them good at economic activities.
In this society, everyone does the thing that they are best at. This is not democratic, but it is what Plato thought the ideal government would be like.