According to Wikipedia the allegory of the cave is “an allegory presented by the Greek philosopher Plato in his work Republic to compare “the effect of education and the lack of it on our nature”. According to Philosophyzer “Plato claimed that knowledge gained through the senses is no more than opinion and that, in order to have real knowledge, we must gain it through philosophical reasoning.” This is the link for the Allegory of the Cave if you want to read about it.
According to Britannica philosopher king is “the idea according to which the best form of government is that in which philosophers rule”.