The deep underlying idea is that if we have to choose a social and political arrangement without knowing the position that we may occupy in society, we will choose fair principles to govern our social and political institutions.
We can commonly observe the opposite effect in society around the world: the people in power often do not choose a fair social and political system. Humans are commonly greedy and would often rather choose something for their own benefit rather than something else that is more beneficial for society as a whole.