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I think the most important thing is to understand how Rawls thinks he can generate substantive principles of justice.

First of all, he wants to reduce the problem of finding principles of justice to a procedural problem. He defines what he calls "pure procedural justice." Here's how it works:

• Perfect procedural justice occurs when there is an independent way to identify the proper outcome and a procedure that always generates that outcome. If we are dividing a cake, the old idea of "one picks and one chooses" gives us a good approximation of the desired outcome nearly all the time. It comes close to perfect procedural justice.
  
• Imperfect procedural justice occurs when there is an independent way to identify the proper outcome but there is no procedure that always generates that outcome. A criminal trial is an example. The desired outcome is that guilty people are convicted and innocent people are set free. But no procedure can come close to producing this outcome all the time.
  
• Pure procedural justice occurs when there is no independent way to identify the proper outcome. The proper outcome is simply the outcome that is generated by a proper procedure. For example, in a lottery the outcome is fair not because the 'right' person gets the prize but because the procedure is fair and it is carefully followed. There is no way to identify the proper outcome except by working through the procedure. Whatever the procedure produces is the proper outcome.

Second, Rawls wants to revive and develop the modern social contract tradition of Locke, Rousseau, and Kant. Rawls' contract is only hypothetical, but it is the basis of his entire theory. The connection between pure procedural justice and the social contract is the idea that if the contract takes place in a properly constructed situation, then the principles agreed to are the 'correct' principles of justice precisely because they have been agreed to or chosen in that situation.