The term "hard science" or "hard SF" is generally used to refer to SF that gets the science right. Or if they speculate on things like wormholes or FTL or femtotech, the speculations are presented in a solid way, without technobabble, and showing the implications for society should such things be developed.
I suggest three sub-categories here: Logical Realism, Scientific Realism, and Social Realism
Logical Realism is when things hang together, and influence each other. This is what happens in the real world. One invention is discovered, and that causes changes in society. e.g. the invention of the car (or the internal combsution engine rather) led to asphalt highways, cheap distribution of produce, a more mobile population, fabulously wealthy oil sheiks, and a serious increase in air polution and road fatalities.
So if certain speculations are adopted, then to write a realistic story or create a realistic universe, one has to follow through with all the implications. e.g. if you have FTL (any FTL) you can have people changing the past, rampant time travel paradoxes and the rest (because an FTL ship is also a time-machine). Or (to use a more familiar example) if you have Star Trek style matter transporters (which do not require time travel or acausality), you also have perfect information transmission over large distances, perfect energy to matter (and vice versa) conversion (why bother with dilithium crystals?), physical immortality (because the transporter keeps an exact record of the person being transported), and so on. The above is a simple example, but one could probably find similar illustrations not only from every single sci fi show ever made for TV and cinema (with the exception of the incomparable hard since classic 2001) but a great many less well thought out novels as well.
Scientific Realism is necessary to avoid the sort of nonsense one finds in TV, movie, and pulp fiction versions of hat passes for Science Fiction. Too often popular Sci Fi script writers show an absolute ignorance of anything to do with science. What is called "sci fi" in the mass media industry is really fantasy space opera, or fantasy mutant creature threatens New York. It is a very different picture to SF written by writers who either are themselves scientists, or if not have at least researched the subject and know what they are talking about. This has nothing to do with speculation regarding future developments (like FTL), but things that are known to be true now.
Thus in popular Sci Fi as well as in pulp fiction novels we find time and again themes and tropes are absolutely impossible, no matter what future developments in science and technology may bring. e.g. the barren desert planet with a breathable atmosphere; "postapocalyptic mutants"; giant monsters not collapsing under their own weight in Earth gravity; super duper ray guns; aliens that look like ordinary human beings, apart from a few token prosthetics like bumps or ridges on the head, or different colour skin, or so on, and speak English, and have an American-style culture; starships or space fleets facing off in two dimensions like naval fleets; instrument panels that explode with lots of sparks when the ship is hit, because they don't have circuit breakers; laser beams that travel slow enough to see, and are visible in a vacuum; and many many other blunders that could be avoided by anyone who knows even high school science. For a whole list of such examples, see Overused Science Fiction Clichés
Again, this is not to criticise these things as escapist entertainment, only to say that they are impossible in the "real world".
Finally, Social Realism is just as important as Scientific Realism, but is often ignored, in favour of stories with superb technological and intellectual explanstions, but flat and unrealistic characters and societies. For this reason, "soft science fiction", so-called not because it is "unrealistic" but because it deald with the "soft" sciences (sociology, psychology, etc) rather than the "hard sciences" (astronomy, physics, chemistry) is just as important as "hard SF". "Soft SF" is also called Literary SF (SF that focuses more on literary style and character than on science or tech), or Humanistic SF (focuses on the personal or interpersonal elements of the story rather than the scientific). Such Soft/Literary/Humanistic SF may indeed be "soft" on realism, or it may just as easily be as "hard" as the best of the "Hard SF" stories. For example Kim Stanley Robinson explores character development in his hard science Mars trilogy
So for realism, SF has to focus on the "social sciences" just as much as on the "hard sciences", and on the humanistic and cultural element just as much as the physics and scientific side of things. And here again pop sci fi and badly written print SF gets it wrong, and there are lots of examples of ridiculous plots that are used time and again, to be found at the Overused Science Fiction Clichés page