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Social Justice Warrirors are people who take offence on behalf of other people, mostly around topics of diveristy, racism, sexism, homophobia, transphobia and so on.
Warriors is the key word in this description. While many regular people are against racism, an SJW will charge into battle to defend against any and all perceived racism, no matter how far of a logical leap must be made. Humor and sarcastic comments are often taken as statements of fact and attacked, causing SJWs to be perceived as humorless cunts.
They are mainly active online, where they can block and censor anyone who challenges their ideas, creating the perfect echo chamber for more furious SJWs to emerge. While they promote safe spaces for people to express themselves, this only extends to expressions which don't criticise their SJW ideas.
SJWs occasionally break out into the real world, bringing their censorship ideas with them. Anita Sarkeesian is a notable example, speaking at the United Nations and being included within 50 organisations on Twitter's Trust and Safety Council.