The world in which we live is deeply, horrifyingly unfair.
Some of that unfairness is inescapable, a consequence of the terrifying randomness and even more terrifying determinism of the universe. Our friends and loved ones are as likely to be hit by buses as our enemies. Babies who haven't even figured out that other people exist yet, let alone tried to hurt them, get diseases that cause horrible lifelong suffering. Market forces tend to amplify initial small disparities in wealth. Trashy reality shows are more profitable than well-written and acted dramas, even though hardly anyone actually watches them.
But a lot of that unfairness was invented by humans, and is entirely under human control. This kind of unfairness can be divided into two categories, which is an entire article on its own, but we're interested today in only one of them, systemic injustice: all of the ways in which the systems and power relations that comprise our society are structurally unfair, even in the absence of deliberate action by any one individual. In other words, for this particular topic we're less interested in unfairness that arises from people cheating, and more interested in unfairness that arises from the rules themselves.
That's where social justice comes in. The idea is simple, its execution hard: create a society in which as much systemic injustice as possible is eliminated or corrected for. More fundamentally, social justice is simply the idea that fixing systemic injustice wherever possible is a major moral imperative. That one is not personally responsible for any particular unfair act is irrelevant; systemic injustice is a problem of a community, rather than individuals, and therefore a matter of communal, rather than personal, responsibility.
Which brings us to the role of criticism in all this, and in particular a specific family of critical schools including the feminist, queer, and postcolonial schools, among others. The common thread is a particular function of critical analysis, namely the identification of ways in which the text expresses, reflects, encourages, or perpetuates systemic injustices. From a social justice perspective, this is an extremely important activity. Texts, after all, are a major component of a culture, and a community's culture is the primary means by which it influences the behavior of individuals within the community. In other words, it is by means of culture that systemic injustices perpetuate themselves, and therefore it is in the realm of culture that they must be met, identified, and combatted.
The primary function of criticism in general, if such a thing exists, could be said to think about culture and engage with it more mindfully. The function of social justice criticism, then, is to engage with culture while being mindful of systemic injustices. Note that this is not necessarily the same thing as criticizing a particular culture; particularly when dealing with works that originate outside one's own community, it's important not to project one's own community's issues onto that other community. That said, the interpretation of a text is as much an expression of culture as the creation of the text, so it is entirely legitimate to look at how a text from one culture might read in one's own culture, as part of a critique of one's own culture.
Ultimately, the goal of this is not to say, for example, "This movie is racist and therefore bad." (Though, of course, there are movies which are bad and racist, including ones where the racism is what makes them bad. But racism doesn't automatically make a work bad, it makes it racist.) The goal is not to attack individual works or creators--though sometimes that is necessary, because one of the ways in which systemic injustice functions is by making it easy to ignore individual acts of injustice--but rather to, as a member of the community, participate in one's communal responsibility to help identify and mitigate systemic unfairness.
The key point here is that social justice criticism is emphatically not about attacking another, because it's not about the Other at all. It's about confronting the darkness in the extended Self, one's own communities and cultures, and exposing it to light so that it can be dealt with. It's about embracing one's own culpability in communal responsibility for the state of the culture, and choosing to be mindful of that responsibility as a first step toward performing it.