But we also want it to behave with some semblance of realism or have its effect on the environment reflected realistically. It moves through the air like a large winged creature, it needs accessways large enough in its lair, its breath can light things on fire, etc.
The elements of the dragon's presence that conform to our understanding of reality (or at least fit in with them) help in the suspension of disbelief.
bingo! We don't have to justify how a dragon exists. The player can accept that (suspension of disbelief). The player should not accept that 20' wide dragons can squeeze through 3' doors. That's not realistic.
If we open the door of unrealistic, we end up playing in a cartoon universe where the kings lives in a burrito hammock smoking albatrosses. It makes no sense. It is unimaginable (well at least not consistently). A non-reality is one in which quite literally, anything can happen. There is no cause and effect. Things can go from being, to non-being, to being something else willy-nilly, and do not make sense in doing so. It's like playing in a world where the characters randomly appear in different squares each round, regardless of their action. And they randomly transform from thing to thing (one minute you're a toaster, the next, you're a human fighter, the next every one is salmon, swimming in tomato soup).
This is the extreme interpretation of "non-realism". Picaso.
Realism is to take the fantasy, and fit it into our known and shared conception of reality. It is, as others have said, to take how things work in our world, and change only a few elements.
That sets every player's expectation. We know how our world works. If you tell me, we're playing in a world, much like our own, set in medieval times, I know what you're talking about. I take our own knowledge of medieval times, and I apply that to your game. When you tell me, "and there's orcs, elves, and magic." I start fitting them in.
That's a whole lot easier than telling me we're playing in a world where nothing is like the real world, and you mean it.
You could call this interpretation, the Macro Realism View. It applies to the game world in general. I suspect most people work this way, and that "realism" arguments are really about this.
Seperate from that is the Micro Realism View. It would cover how the game approaches realism to individual aspects, like combat, movement, eating/sleeping/fatigue, falling damage, drowning, etc. For the most part, we all know there's a trade-off in how closely real-life activities are simulated in a game. Usually it's a matter of game balance, fun, and speed.
If somebody's complaining about "realism" in relation to Micro, it's usually a matter of it wasn't realistic enough (usually in that the player didn't like the result), or it was too realistic (usually in that the player didn't like the result).