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The shadows on the wall represent an illusion of reality that the people viewing the wall try to interpret without understanding the truth; that the shadows are only shadows. The viewers of the wall have never genuinely seen what the objects which cause those shadows look like. To the viewer of the wall, all of reality is represented by shadows. The allegory is a social commentary about understanding what the true nature of the world is, and how many people never see it because of the beliefs of the society they are raised in. If you had been raised in the thirteenth century your culture's world view (your cave) would have had shadows which led you to believe that the Earth was flat and that it was the center of the Universe.
When Plato speaks of being blinded by the light of the fire, or the sun upon leaving the cave; he is discussing the way in which some people will react violently when their cultural world view is challenged to the core of their fundamental belief system. Some people would rather retreat back into the cave than have to first acknowledge, then adapt to the fact that everything they knew was wrong.