I think there have been some excellent points made in this thread overall... However it seems not one of us has offered an actual objective definition of what it is.
I think the general consensus is that Social Justice Warrior is either a derogatory term used too readily to defend dubious ideals, or, its an apt identification of somebody who takes PC to the extremes. Those are what I would term subjective definitions of the term.
What I would be interested in is if there is an actual objective definition. I think the real definition of a SJW is somebody who will use any modality of communication in order stir up the pot or "raise awareness" if you prefer, and basically leave others to sort it all out. They remind me of food critics, they'll sit and eat a meal, rip it to shreds and the laugh is, if you asked them to make you scrambled egg on toast, they'd probably make a balls of it. To me that is a social justice warrior. Somebody who makes the ammo, but gets someone else to use it. Which is why I find a lot of these PC mouthpieces utterly deplorable, they can talk the talk but don't walk the walk.
Only certain types of reactionary people use it derogatorily at all. Unfortunately, that seems to be most these days. Originally, it was a very honourable thing to be called.