"Doubtless they would."
"Again: if their prison house returned an echo from the part facing them, whenever one of the passers-by opened his lips, to what, let me ask you, could they refer the voice, if not to the shadow which was passing?"
"Unquestionably they would refer it to that."
"Then surely such persons would hold the shadows of the manufactured articles to be the only realities."
"Without a doubt they would."
Plato (in the person of Socrates) then considers what would happen if the course of nature brought to the prisoners a release from their fetters and a remedy for their foolishness, and concludes as follows:
"Now this imaginary case, my dear Glaucon, you must apply in all its parts to our former statements, by comparing the region which the eye reveals, to the prison-house, and the light of the fire therein to the power of the sun; and if, by the upward ascent and the contemplation of the upper world, you understand the mounting of the soul in the intellectual region, you will hit the tendency of my own surmises … the view which I take of the subject is to the following effect."
Briefly, the view taken is that the "Form of Good" perceived by the mind is the source of everything that is perceived by the senses. This is equivalent to saying that the objects of our three-space world are projections of higher-dimensional realities—that there is a supernal world related to this world as a body is related to the shadow which it casts.