In Rawls's original position, a constraint that hides from the parties facts such as their race, class, gender and talents, so that principles of justice are chosen without regard to personal advantage.
In more detail
The veil is a device of representation: it models fairness by preventing arbitrary facts about citizens from influencing the agreement. Rawls argued that parties behind it would choose equal basic liberties and the difference principle. Critics question whether people so deprived of knowledge could choose at all, and whether the outcome depends on assumptions built into the device.