You, a mere mortal, encounter P, some super smart alien. Or maybe it's a supercomputer, or maybe a god; versions of the paradox differ on this. P comes up to you and says: "I have a deal for you. I'm going to give you two boxes--box A, and box B. Box B is transparent, and you can see $1,000 in it. You can't see what's in box A. I'm going to give you two choices. The first is to take box A--you get whatever is in it. The other choice is to take both boxes--you get box A, plus the $1,000 from box B."
So, you ask, why don't you take both boxes, getting the free $1,000? Well, says P, there's a catch: "I have predicted whether you will take one box or two boxes." (Or maybe I've simulated all of the atoms in the universe, or maybe studied your psychology, or maybe something else--versions of the paradox differ in how P knows how many boxes you're going to take. But however he knows it, you believe him; maybe he has, in the past, predicted everyone who's taken this challenge successfully.) "So I know what you're going to do", says P, "and before you arrived I decided how much money to put in box A. If I predicted that you were going to take only box A, I put $1,000,000 in it. Otherwise--if I predicted that you were going to take both boxes--I left box A empty."
"So", says P, "How many boxes do you want to take?"