"A Queen never leaves her throne" suggests that a person of regal stature, metaphorically representing someone who carries themselves with confidence and self-assuredness, does not allow themselves to be pulled down by the actions or words of others.
"To address a peasant throwing stones" implies that even when faced with insults, criticism, or negative behavior from others (symbolized by the "peasant throwing stones"), a person of strength and grace should not stoop to their level or engage in confrontations.
This saying advises individuals to rise above petty conflicts and maintain their sense of self-worth and dignity. It reminds us that reacting to negativity with further negativity only diminishes one's own stature.