A reference to Ayn Rand's "Atlas Shrugged" where the society's creative leaders (inventors, artists, captains of industry) go on 'strike' to "stop the motor of the world" and lead to the collapse of the collectivist society portrayed in the novel.
'Going Galt', then, refers to taking your (economic) ball and going home.
Ironically, the people most likely to use this phrase are those who's economic contribution could be best described as limited.
A: "I can't believe that communist Obama with his socialist policies might get re-elected and raise the marginal tax rate by 3%! I'm going Galt!"
B: "But your job as an internet troll doesn't pay you anything and I don't think you know what most of those words mean".
A: "You're violating my first amendment right to freedom of speech! Fascist!"