It's not a universal opinion that "realism" = "better". How can the imagination become involved if everything is real? How can new concepts be explored if we are anchored to the old? These are valid concerns, especially when it comes to fiction (which is necessarily "unrealistic", at least in a few senses such as specific details). However, I would say that "reality" serves as the foundation for every series, no matter how apparently-unrealistic it is. This manifests in a few different ways.
1: Immersing the audience in the story. (SENSES)
One of the primary obstacles that media has to overcome is its inherent nature as a sense-limited medium. Media can depict two senses in an incomplete manner (sight and sound) and has no way to connect to the other three senses (smell, touch, taste). Of course, the characters in the story are generally depicted as possessing all five senses. To fully "immerse" the audience, the product must attempt to bridge this gap by using things like effects and character reactions to depict the "full" conditions.
The effects of this can be seen by the way that things like games and movies are described. More immersive material will have descriptions like "bone-crunching" or "nauseating", while less immersive fare feels "floaty" or "weightless". Fight scenes attempt to create a sense of actual damage and consequences, and a scene that's clearly faked, with no hits connecting, may suffer as a result. This also applies to things like props or object design: if an object feels tangible, like something that could conceivably be real, it will make a stronger impression on the audience.
This is not to say that fantastic elements can't be included, but there are some baseline assumptions that audiences make about a movie. Humans behave like humans, and are affected in ways humans are. If you cut them, they bleed. If you blow them up, they're full of guts and organs and don't come apart like a cartoon character. Even a fantasy series can benefit from this "grounded" design: it's easier to imagine damage from a sword or mace if you connect it to more plausible or relatable damage, like being cut by a knife or hit by a rock.
The goal of this point is twofold: to connect the character to the audience by sharing their experience, and to connect the audience to the world by showing them what it would be like to be in such a situation. There are many ways this can manifest, but all of them should revolve around overcoming the barriers between "real" senses and "depictable" senses.
2: Making the story internally consistent. (LOGIC)
In commentary for Aliens, James Cameron remarked that the movie works in large part because everyone takes it seriously, and thus it convinces the viewer that these characters are concerned about their lives in a very serious way. This is what internal consistency should support. In actuality, none of this is "real", but the trick is drawing in the viewer so that it seems like it is - and it should be real, at least to the characters.
Generally, making a fictional story requires a veneer of "real", even if it's not in the sense of matching our reality. That is to say, the story must be real to the characters. One of the problems with plotholes and other issues of logic is that it damages this glamour. We are meant to believe that these characters are doing something important to them, even to the point of being life or death. When characters make inexplicably bad decisions to create tension, it makes the story feel more fake overall, and generally leaves fans scrambling to find or create an explanation for it. While a delayed reaction may not be so bad ("Hey, that didn't make sense"), more obvious plot holes will immediately pull the audience out of the action.
Magic, in particular, is a thorny obstacle in the way of internal consistency. The Harry Potter series has many examples of objects that create plot holes, most famously the Time-Turner. This was an object that allowed for time travel, but was only used for one plot-related activity. It was primarily relegated to the simplistic purpose of allowing a student to take more classes than normal. The reason for this under-usage is never explored, and in light of it the entire story is diminished. All the drama and tension could have been for nothing if they remembered to use the obvious magical artifact that can solve everything.
It can therefore be said that the most important part of this point is making a world believable, and overcoming the natural barrier between "this is fiction" and "this is a story that I am invested in". Like any other design decision, it can make the difference between a sensible story and a story that can't be taken seriously (not that this stops people who are fans of Harry Potter or any other plot-hole-possessing series, of course).
3: Making the story relevant to reality. (MORALS)
This is, in my opinion, probably the least important aspect of the concept of believability. However, I mention it because of how often movies, shows and games try to have a "message" that pertains to real life regardless of how unrealistic the media itself is. The basic idea when dealing with morals or lessons applied to real life is this: every change you make to necessitate the moral is one step away from the moral actually being applicable. In some cases, this is more obvious than others - extreme cases that use ridiculous or fantastic logic to justify a change in real behavior. However, many "morals" are just as nonsensical underneath, yet appear normal on the surface. I have several examples of "lessons" that fall short due to varying factors.
Metal Gear Solid 4: Attempts social commentary on current events. Fails due to a lack of understanding regarding everything from sociology to economics to technology. Most unfortunately, the relative lack of context means that many players feel that it's "accurate" or "enlightening" despite its myriad liberties with plausible material
Chrono Cross: Attempts a green aesop about humans destroying the environment despite the fact that it takes place on a completely different world where humans live in small villages and the world is largely verdant and green. In short, an attempt to comment on reality that makes no sense in-universe.
1984: Shows the horror of a totalitarian world by using implausible/impossible technology and control. Exaggerates the level of control possessed by a totalitarian regime in some ways that could have easily been depicted accurately and been just as horrifying (secret police, curfews, etcetera)
X-Men: Attempts to connect "mutants" with "homosexuals" - as in, they are unfairly persecuted, "coming out" to parents is difficult and divisive, etcetera. The difference is that mutants possess dangerous powers that could endanger the lives of other people, and homosexuals do not.
The value of a lesson relies on its plausibility. There are many examples of stories that attempt to carry a lesson that are derided for their unlikeliness and obviously impossible natures, such as the Chick Tracts promoted by Jack Chick that claim that various activities and lifestyles lead to pacts with Satan and so on. The reason these "lessons" don't work is because they don't make sense. Therefore, if such things should be held to that standard, then all media that attempts to comment on real life should be treated the same.
These three examples do not just apply to "totally realistic" products. They add a distinct layer to all forms of media, and provide universal, objective connections to the audience. This blog does not exist to debate the finer mechanics of "why" realism is good in and of itself; rather, it is the goal to explore how realism and believability can make a piece of work more credible and immersive.