Its called a theory of justice for a reason you know
But it is applicable to the modern society.
Anyways to put it as simply as possible, justice in a country must be considered from an impartial position. If we forget who we are at the moment and what we are, our social class or intelegence our strength etc then we can formulate a position or structure that is fair for all because we will not tailor the rules for a given group. That is called a veil of ignorance in his works, i cant put it any simpler then this. This is taken as the starting point of his work.
Now moving on, since we dont know anything about ourself under the veil, there are some ground rules that we need to lay out for the society which everybody must absolutely have without question. That is called basic liberties. So everybody has access to basic liberties. Sounds fair enough?
The second principle states that when you have access to basic liberties(again this is not only liberties in the classical sense but to many other things beyond that), then how do we distribute everything else ? Rawls believes that everybody must have not only the RIGHT to participate for any other benefit of the society but also have equal chance to recieve it if his natural abilities are the same.
Then again, rawls understands that inequalities do exist in the modern world, so we should limit the inequalities in our societies to the ones that serve the worst off not the best off because its not 'fair' when the society gets more benefits while the worst off recieve a lot less. By guaranteeing the worst-off in society a fair deal, Rawls compensates for naturally-occurring inequalities (talents that one is born with, such as a capacity for sport).
Also Rawlses ideas need to be considered with Social Contract in mind when all parties are here to find a peacefull way of coexistance of sorts which is acceptable for everybody.