"What do we talk about when we talk about justice?"
Justice is not something that is the exclusive domain of courts; and, indeed, that law and justice are often at odds and have nothing to do with each other. Justice is at one level a societal compact or contract, and it binds every one of us. It takes various forms, from the legal justice we know of to gender, race, class, urban planning ('spatial justice), and more.
At another level, it is an individual commitment, because like any contract, it involves two players: society one the one hand and individuals on the other. The 'society' could be anything, from a large and amorphous ideal to a more tangible neighbourhood-watch group.
What defines us, as human beings, and as a society, is this concept of justice.
There are only two things that separate us from the animal kingdom: justice and torture; for humans are the only creatures that derive pleasure from the deliberate infliction of pain, for its own sake, on their own kind; and, like justice, torture takes many forms. Torture is injustice. Racism is both injustice and torture.
if we are to advance towards 'civilization' -- not retreat from it -- then we are required to hew to increasingly difficult and higher standards of justice, following an ever-advancing evolution of what, in law, and in the Bible and other ancient texts including Buddhism, is essentially the 'neighbour principle'.