The shadows represent a false vision of the truth, an illusion about reality. Because the prisoners have never seen the true objects that exist in the world, the objects which are casting those shadows, they believe the shadows are all that is. Plato represents the philosopher with the brave prisoner who climbs out of the cave to discover the real world, and who wants so badly for his fellow prisoners to know the truth, that he voluntarily climbs back into the cave to tell them. But they kill him for this because they don't want to have to change, to adapt to a higher truth. The shadows represent false ideas that people live by in this world, or materialism, or whatever, and the objects represent the pure forms that Plato speaks of in the Republic. The form of the good, the form of beauty, truth and goodness. The prisoners are so used to the false world they have come to live in, that they can't handle the truth.
If you've seen the shawshank redemption you will remember how the prisoner who gets let free at the end is so unsure of what to do with his newfound freedom, so used to life inside the prison walls, that he hangs himself. Something like this is going on analogously in Plato's Allegory of the Cave