Setup: An entity called Predictor can predict your actions with 100% accuracy. You are given a choice between taking the contents of two boxes or the contents of just the first box. You know that one week ago, Predictor determined your choice and filled the boxes with money according to the following rule. He put $10,000 in the second box and if he determined that you would take both boxes, he put no money in the first box, but if he determined that you would take just the first box, then he put $1,000,000 in the first box.
The paradox arises when you are asked to choose one box or two boxes with the intent of maximizing your gain. Wether the first box is filled or not, you will get more money by taking both boxes, so the principle of dominance says to take both boxes. But since Predictor knew you would take both boxes, he put no money in the first box.
The problem here is that we don't all agree on whether the universe is truly deterministic. If we assume that the universe is deterministic, then the best choice is definitely to take only the first box. The reason for this is that in a deterministic universe, it is actually possible for your choice to cause the money to be placed in the first box. Normally, we don't think of causation extending backwards in time because it rarely happens, but that is exactly what prediction does.