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I have been researching the veil of ignorance. As near as I can tell, here's what the veil conceals and what it does not conceal.

The Veil of Ignorance

• People do not know what their personal characteristics will be. For example, whether they will be male or female, black or white, strong or weak, and so forth.
  
• People do not know what position they will occupy in society. For example, they do not know whether they will be upper class or lower class.
  
• People know that in real life they will have some conception of the good, but in the original position they do not know what that conception will be.
  
• People know that there are certain "primary goods" like wealth and self-respect that will be useful to them no matter what their conception of the good turns out to be.

I think Rawls has a clever idea here. He knows that one of the problems people have when choosing principles is that their self interest may bias their judgment in one way or another. The veil is supposed to make it impossible for certain kinds of self interest to operate. People in the original position are still self-interested in that they want to advance their notions of the good. But they don't know what their notions of the good will be in the 'real' world; and they don't know their position in society. They can't choose principles that will favor themselves because they don't know what sort of person they will be.

Notice also that people in the original position cannot use what some game theorists call "threat advantage." Someone uses their threat advantage when they threaten to simply withdraw from a negotiation and let the others fend for themselves. In an initial situation in which people knew what skills and other strengths they had, the better endowed could simply threatened the others with abandonment. The veil of ignorance make the use of threat advantage impossible.