Put The Left Brain In
Where science fiction is an exercise of speculation and problem solving by the right brain, fantasy is an exploration by the left brain of the implications of faith. The discovery of facts, the deep processes of inductive reasoning so inherent to science fiction, are irrelevant in fantasy. The facts are often known in all their essential entirety from the first minutes of the story. It's why prophecy usually plays a role at the beginning and the climax usually revolves around a hero achieving moral rather than intellectual certainty.
Note that nowhere are swords and sorcery a requisite of fantasy, and neither does the genre preclude death rays and spaceships generally considered the obvious distinction between fantasy and science fiction. The Star Wars trilogy is a fantastic example of fantasy tossed into the wrong bin because of lasers, aliens and space armadas. But it strictly is no more science fiction than The Lord of the Rings or Harry Potter. All of the pseudo-humorous ribbing at the edges of Star Wars about things like how many civilian contractors the Rebels must have massacred in the assault on the second Death Star, these jabs point out precisely the sort of story concerns that science fiction deals with. Nowhere in Star Wars are the implications of technology explored, it is merely the window dressing for a morality play.
This isn't to say that fantasy is the intellectual light weight of the two, nor am I trying to argue that fantasy is just science fiction with plot holes. It is simply concerned with different issues. Luke does not figure out how to destroy the Death Star, he does not deal with the implications of destroying the Death Star. The Death Star exists so that he can take a leap of faith and shut off his targeting computer. The existence of the Death Star, the how and the why, are all beside the point. It could be a planet killing meatball for all the difference its nature makes.
If Arthur C. Clarke was right, and any sufficiently advanced technology is indistinguishable from magic, then a corollary might be added, that any sufficiently advanced being is indistinguishable from god. Fantasy is concerned with what it takes for man to come face to face with his gods, hinging on the moment of moral crisis when logic and reason fail.