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I was curious about what Rawls means by "rational" and "mutually disinterested."

Here is part of what he says about the rationality of the people in the original position.

I have assumed throughout that the persons in the original position are rational. In choosing between principles each tries as best he can to advance his interests. But I have also assumed that the parties do not know their conception of the good. This means that while they know that they have some rational plan of life, they do not know the details of this plan, the particular ends and interests which it is calculated to promote. How, then, can they decide which conceptions of justice are most to their advantage? Or must we suppose that they are reduced to mere guessing? To meet this difficulty, I postulate that they accept the account of the good touched upon in the preceding chapter: they assume that they would prefer more primary social goods rather than less. [Theory, section #25]

So each of the people in the original position is rational in that they want to pursue their own interests. No one can pursue very specific interests because they don't know their specific idea of the good. (That's part of the veil of ignorance.) But they know that they will need so-called "primary goods" that can be used to advance their interests. Some of the primary goods are "rights and liberties, powers and opportunities, income and wealth." [Theory, section #11]

Being "mutually disinterested" means that the people in the original position "do not seek to confer benefits or to impose injuries on one another; they are not moved by affection or rancor. Nor do they try to gain relative to each other; they are not envious or vain." [Theory, section #25]