"Social Justice Warrior", often abbreviated to "SJW", is a term used on the internet, usually in a pejorative manner, to describe people who are seen as overly concerned with issues of social justice. It is mostly amongst younger people, and generally on micro/instablogging sites such as tumblr.
While being socially conscious is not a bad thing, the opposition to Social Justice Warriors comes from the fact that they often use overly-academic jargon, criticize things from an unrealistic standpoint, and often use social consciousness as a vehicle for smugness. To paraphrase Andrew Hussie in Homestuck (speaking through Porrim Maryam): a social justice warrior is someone interested in deconstructing every conceivable, hypothetical form of injustice, no matter how obscure, except those which are actually important. A Social Justice Warrior is perhaps the same as what was once called the politically correct, only no one ever used that term except for Republican Uncles.
Of course, the internet being what it is, "Social Justice Warrior" can often be used as a ad hominem strawman attack, to discount people who are bringing up important, relevant issues as being simply neurotic and smug.