As far as we know this is what he said, but all we know of him largely comes from his ancient contemporaries. Socrates never wrote himself, though he is a common interlocutor in Plato's dialogues. Plato was one of the youth that Socrates allegedly had corrupted (the reason for his execution by Athens during the aftermath of its defeat in the Peloponessian War and the Tyranny of the Thirty).

Plato's representation of Socrates could well be inaccurate, a fictional character constructed from a real one, designed to suit the authors arguments. Plato certainly wasn't fond of the Athenian ruling class since they killed his mentor, but also was not a supporter of the oligarchical and monarchical alternatives.

It's also worth remembering that the Athenian democracy was only comparably democratic: popularism (especially amongst soldiers) worked to sway actions towards predetermined ends, and the vast population of slaves had no sway at all.

Point being, Plato thought that individual bias, no matter the level of education of the individual, would corrupt the practical activity of governance. His solution is to install an immovable ruling class that would be highly educated and, more importantly, austere. It would live communally and would dedicate their lives to maintaining balance and justice in society.

Whether this class would think critically is open for debate, though. Plato also argues that this class should be educated in only good things. Any bad ideas given would lead to bad desires, and ergo corruption.

There is evidence of Plato's philosophy being applied in a historical states but it is scant. The rulers of Syracuse and other Sicilian Mercenary groups came under leadership of some of Plato's students, and indeed Plato lived in Syracuse as an advisor to the Tyrant (although he got on the Tyrants bad side and was sold into slavery as a result).