Hard Sci-Fi
From Zanecorpwiki
IMO, hard sci-fi is a term most appropriately applied to fiction which--as far as we know--presents a possible future and part of the story involves how that future is possible. In other words, science plays a key part in the story.
This is contrasted with other sci fi which is closer to fantasy and contains significant fantastic elements. Note that fantasy and "fantastic sci-fi" need not be extraordinarily impossible. For instance, the "Culture" universe of Ian Banks, and the nano-tech universe of Alastair Reynolds are some of the more fantastic futures in terms of what's possible for people to do. However, the science behind the future is explicit and--at least attempts to be--consistent.
This is contrasted with something like Cowboy BeBop or Firefly in which the universe depicted is actually quite simple. The lifestyle of the characters almost bucolic. However, the science behind all this is weak or non-existent. From a science point of view, big questions go unanswered, and there are often inherent contradictions or problems. The most common science issues are deal with faster than light travel and communication.
To the "hard sci fi" adherent, this kind of sci fi is really just fantasy in a futuristic setting.
Most sci fi exists in a vast middle ground--and it's actually hard to find examples of truly meticulous "hard sci fi". There's always some point, some question that if you push hard enough, is really hard to explain. Good sci fi has to focus primarily on story and characters because it's fundamentally a story. Maybe there's a fetish genre of "geek sci fi" that actually focuses on reeling out specifications and formulas, but I've never seen the idea outside of the context of a joke. In most people's world view, that type of stuff would be outside of sci-fi altogether, hard or not.
Star Trek is a great example of a middle ground. Science definitely shows up in the show all the time and plays an important role. It's not quite hard sci-fi, though, because much of the science is soft. It's a common joke that whenever the writers of a Star Trek episode get stuck, they just invent some new magic particle to solve everything. "If we could only rig up of gluco-tachy-itron field, it just might kill the alien infestation!"
