Can someone explain Zeno's Paradox of Motion?

I will do my best to explain. Zeno's paradox is counter-intuitive to nearly everyone because we disregard it's logic every day. Another simpler variation of Zeno's paradox erts that a man walking toward a wall will never reach it. Why? The logic goes like this: he will eventually walk 1/2 the distance to the wall. Once he has walked half the distance, he will eventually walk 1/2 the new distance. And so on, ad nauseum, always having another half-distance to cover. Of course we all walk to walls everyday, so the counterargument to this logic is "proof by demonstration".