Isaac Assimov and Arthur C. Clarke, who were part of the Big 3 in sci-fi, are two of the earliest authors in the hard sci-fi genre. They also exemplify some of the difficulties with extrapolation and hypothesizing future inventions, which can make their works feel quite dated.
If you know the how and the why of phenomena, you've probably got yourself some hard sci-fi. If things are a little magical and unexplained, focusing mostly on the mental and social aspects, then it leans toward the soft side of the scale. There is some gray area in the middle. Sometimes, what is dressed as hard, scientific fact is just plain our silly magic. If someone explains in great detail how a ship moves at or faster than the speed of light, you've got a strange ambiguity on your hands. Modern science states than any object with mass travelling at such a speed would do so at infinite energy expenditure and enlarging to infinite mass. Or the object would go back in time. Which would really upset everything. So while someone may use or even explain "warp speed", it just isn't real. But somethings have to be different or unreal if the book is science fiction, right? Or else you just end up with fiction.
The genre has suffered since the 50's and, with it, Disneyland's Home of Tomorrow. The expectations of hover cars and robotic nannies featured in Jetsons are a long way off if anyone ever gets around to them. Computer hacking, genetic splicing and cloning, and biological warfare are the subjects of modern hard sci-fi.
I am not passing judgment on whether one end of the spectrum is better than the other. Hard science fiction can be fascinating because the hypothetical has a chance of becoming the real. I also find that hard science fiction writers take their readers a little more seriously, anticipating our rigorous and analytical questions and probing in ways that the early Star Trek and Star Wars actors and writers could never imagine. But hard science fiction can also be tedious and overly pedagogical. The trick is to find a balance between the science and the fiction, not forsaking one for the other.
The Mars Trilogy