What does this story mean? Plato himself provides the answer: he has the interpretation immediately follow the story (517 a8 to 518 d7).

The cavelike abode is the "image" for τὴν ... δι' ὄψεως φαινομέντην ἔδραν, "the place of our dwelling which (in an everyday way) is revealed to sight as we look around." The fire in the cave, which burns above those who dwell there, is the "image" for the sun. The vault of the cave represents the dome of the heavens. People live under this dome, assigned to the earth and bound to it. What surrounds and concerns them there [120 {GA 9: 214}] is, for them, "the real" ["das Wirkliche"], i.e., that which is. In this cavelike dwelling they feel that they are "in the world" and "at home" and here they find what they can rely on.

On the other hand, the things that the "allegory" mentions as visible outside the cave are the image for what the proper being of beings [das eigentlich Seiende des Seienden] consists in. This, according to Plato, is that whereby beings show up in their "visible form." Plato does not regard this "visible form" as a mere "aspect." For him the "visible form" has in addition something of a "stepping forth" whereby a thing "presents" itself.a Standing in its "visible form" the being itself shows itself. In Greek, "visible form" is εἶδος or ἰδέα. In the "allegory" the things that are visible in the daylight outside the cave, where sight is free to look at everything, are a concrete illustration of the "ideas." According to Plato, if people did not have these "ideas" in view, that is to say, the respective "appearance" of things — living beings, humans, numbers, gods — they would never be able to perceive this or that as a house, as a tree, as a god. Usually they think they see this house and that tree directly, and the same with every being. Generally they never suspect that it is always and only in the light of the "ideas" that they see everything that passes so easily and familiarly for the "real." According to Plato, what they presume to be exclusively and properly the real — what they can immediately see, hear, grasp, compute — always remains a mere adumbration of the idea, and consequently a shadow. That which is nearest, even though it has the consistency of shadows, holds humans captive day after day. They live in a prison and leave all "ideas" behind them. And since in no way do they recognize this prison for what it is, they consider that this everyday region under the dome of the heavens is the arena of the experience and judgment that provide the sole standard for all things and relations and fix the only rules of their disposition and arrangement.

a Offprint from Geistige Überlieferung, 1947: Being present, i.e., being near [An-, d.h. berzu-wesen].