What is Justice?

If someone were to ask me this question last year I probably would have answered with "justice is doing the right thing." But the more we discuss in class and  read The Republic I realize I don't really know what justice is.
There's so many different definitions of justice. I mean mine still is doing the right thing. But what does that really mean? The way I interpret doing the right thing as might be entirely different to someone else.
But no matter what definition justice is given I think it's a very important part of having a stable society. A society without justice, at least the justice decided upon by the majority, would be chaotic. This kind of reminds me of Freud's theory. Without the ego and the superego (justice) to keep the id in check people would be doing whatever they felt like doing whether it was destructive or not.
Even if Adeimantus and Glaucon are right that people only do the right thing when it benefits them or because they are afraid of the consequences, at least they are still doing what is considered right. No matter what someone's reason for being just is, the way I see it, as long as their being just that's all that matters.