Literal answer: The enigmatic key character in Ayn Rand's book "Atlas Shrugged." He is a genius who invented a motor that functions with revolutionary technology, that would have entirely changed all of the industrial world as it was known at the time. However, a genius caught up in an increasingly collectivist society that touted proclamations that genius is evil, mankind's mind is immoral, and all people should immolate themselves to the common good of their brother, he abandons his motor and "disappears" from society. Throughout the course of a decade, he also prompts many other great inventors, thinkers, workers, scientists and industrialists to leave society also. He refuses to live by the standards that his society were preaching at him, and, also refuses to lend them his own logic and mind. He claims that this is because he is just giving society what they asked for--a world without great minds that stand above "average minds". In part of an address he gives to his society near the end of the book, he claims of his own personal philosophy and the reasoning of those that left with him,
"I have removed the source of all those evils you were sacrificing one by one...I have deprived your world of man's mind...we are on strike against self-immolation. We are on strike against the creed of unearned rewards and unrewarded duties. We are on strike against the dogma that the pursuit of one's happiness is evil."
In the end, it is the theories that Galt stands against that does indeed "stop the motor of the world," and it is left to Galt and some of his closest friends to attempt to rebuild the world as they feel it should be.
On a more symbolic level, the question "Who is John Galt" becomes a catch-phrase that everyone in the novel uses as a sort of "who knows?" shrug-of-the-shoulders at things that they cannot explain. If one were to ask, "Why is the world the way it is?" the response would be, "Eh-who knows? Who is John Galt?" as a sort-of "nobody really knows" answer. The irony in this catch-phrase is that as soon as the world learns who John Galt is, the answers to all of those questions of why the world is was as it was are exposed. Galt reveals society and the politicians for who they really are, answering how the world came to be as it was. He strips them of their veneer of virtue and exposes them as power-hungry politicians who use the world to achieve their own ends. So, answering the question of who John Galt is also ends up answering the original question that prompted the catch-phrase.
Literally and figuratively, John Galt represents Ayn Rand's ideal philosophy of human happiness, and that is that reliance on one's own mind and genius to improve the world and quality of living is the path to true success and innovation.