To me the hard science moniker requires that the story depend on science that is both plausible (if not presently accepted) and internally consistent. The science is plausible when it cannot presently be proved impossible. Faster than light travel is usually considered plausible, even though its development is doubtful for many reasons, not the least being Fermi’s paradox. Time travel, less so. Mind control, including telepathy, telekinesis, or prescience, is firmly implausible, and not just because no brain mechanism exists—Las Vegas would go broke in a world where anyone held such powers.
To contrast, fantasy employs what I think of as magic—mechanisms that vary from fantasy world to fantasy world, and whose limitations are sometimes not fully explained. Such magic is often in the form of supernatural powers exercised by a character. In these fantasy worlds, people are not simple chemical machines, as they are in the hard science world. In Star Wars, for example, the force is one such magical mechanism. In recent offerings in the Star Wars franchise, Lucas has made a half-hearted attempt to give the force a physical basis, but its appeal remains as fantasy—a mysterious power arising from within the characters.
A story disappoints me if it pulls a rabbit from a hat. I want to grasp the boundaries of the story up front so that I have a chance to participate. If I’m going to play the game, I want to know the rules. If a deus ex machina unexpectedly resolves the otherwise intractable mess the plot has become, that’s bad storytelling. For me, the magical framework of a fantasy story notifies me that rabbits will unashamedly be pulled from hats.
So one may naturally ask, “Is science knowledge necessary to appreciate hard science fiction?” I would say, “No, it’s the other way around.” Science knowledge makes it difficult to appreciate other forms of speculative fiction. If a reader has a firm belief that the principles of physics, chemistry, and biology underpin reality, fictional worlds that don’t conform to these principles are just pretend. Sure, all stories are pretend, and as readers we willingly suspend our disbelief—to a point. If a story demands too much forbearance, for example by relying on too many coincidences or on unrealistic actions by its characters, we loose patience and turn from reader to critic. Someone with a science background who reads a story that relies on the supernatural powers of its characters has already had to choke back a great deal of disbelief—perhaps beyond their limit.
Readers unschooled in science may have little difficulty with hard science fiction. A good hard science fiction story may be no more difficult to follow for them than a sword and sorcery adventure. It will depend on how well the author explains the science, and how important understanding it is to following the plot and understanding character motives.