I sum it in the term "warrior". A warrior is someone that fights, but that can be both good and bad. Captain America fought to protect others, Thor started wanting to show off and get glory. A warrior monk would say violence might be a necessary last resort, a neocon hawk might want to bomb a country that looks at us funny.
To me a social justice warrior is someone that skews closer to the second choices in the sets. They're aggressive, angry, uninterested in middle ground and understanding, self victimizing, and usually out for some personal gain. Or in other terms, they're life isn't perfect, but all they want to do is wallow in self pity about how someone is keeping them down instead of building themselves up. The spout about empathy but show none to their opponent. They criticize, but hate being criticized. They're most active where the press coverage is, to the determent of lessor known issues (ie black Captain America = great move for diversity, the nearly all minorty team of Avengers = no one cares.) They dogpile on minor slights and faux pas. And at the worst end, they seem less interested in the end goal than in getting attention, either by the complaints themselves, on in the only acceptable solution being something big and profound (ie: who cares about ubisoft giving us a female lead in child of light if they didn't in Assassin's Creed). Oh, and it's also a bit of an ironic term, as warriors are mighty and face adversity, while SJWs are only mighty behind twitter, tumblir, or in safe spaces, and their causes are often about how little they can handle an outside reality that might trigger them.
Yeah, it's a bit of a pejorative to shut down someone, but for me, it comes out when someone needs to be stopped. they've shown no desire to meet in the middle and are just trying to vilify, guilt, shame, and otherwise yell at people until they get full agreement. The guy that emailed Nintendo about including gay marriage in Tomodachi life wasn't an SJW. The people that shouted homophobia, passed along misinformation about the bug originally patched out, and wrote lengthy editorials about how "problematic" is was that nintendo didn't affirm their orientation, that's SJW territory.
We need fewer social justice Warriors and more Social Justice Diplomats.