Yeah, but to elaborate on this explanation a little more ... because it's what finally made me understand. Look at it slightly differently:
Let's say he offers you the chance to switch from the ONE cup you chose to BOTH of the other cups prior to him flipping over anything, then he'll flip over one of them that doesn't contain the diamond after you switch. You wouldn't hesitate, right? You would know that your chances would go immediately from 33% to 67%. Well, that is exactly what he did, he just flipped it first.