I think we need to expand somewhat on @Galastel's answer. Specifically two concepts: Immersion and Suspension of Disbelief. Because that is what it boils down to, in my opinion.
So. Immersion. This is about drawing people in, and keeping them drawn in. This can apply to games, stories, music, what have you. And what it essentially boils down to, is the ability to feel like this world crafted feels real to the audience.
Let's take a weirdly specific example. The Roman Empire in the first century. If viewed wholly from a historical lens, what do we know about it? Damn near everything. From the quality of the roads, to the locations, to trade routes, to the price of a bushel of wheat, to the lives and treatment of women, to the lives and treatment of slaves.
We know a lot about their battle tactics (though there is still oodles of debate on this subject). We know which battles they won, and which they lost. In the end, what this means is that if a historian wants, they can get utterly absorbed into the world that is first century Rome.
So apply this to, say, The Lord of the Rings. There is enough detail to the world, allowing for the reader to be immersed. But there is even more details to the Tolkien buffs to gush about and debate about and discuss for days on end. There's languages to learn and customs to observe and places to go and people to meet
Alright, now onto Suspension of Disbelief. We, the readers (consumers) (generally) know it's a work of fantasy. We agree going in that this can well be a departure from reality as we know it. That's the point, we want to get away from gritty reality.
So we sign on, knowing this is going to be out there on some level. As long as it is internally consistent (and therefore doesn't break our immersion) we're usually fine with it.
We want to believe that Harry is 'the chosen one' (TM). We want to believe that Khaleesi is the mother of dragons (TM). We want to believe that Mario really can dive into pipes and kill Bowser's minions by jumping on their head.
As long as the tale is internally consistent, we are willing to handwave the specifics ('the black box' as was mentioned in @Galastel's answer). And this can be done well. (see Brandon Sanderson's lectures on Hard vs Soft magic systems).
But the second you introduce a power just for the sake of Deus Ex Machina, only to never use that again? Like Timer-turners in Harry Potter (that could have sent someone back in time to kill Tom Riddle in his youth and saved countless lives, and isn't that convenient that all the Time-turners were mysteriously destroyed), or those incredible spells Gandalf uses only once, and then never again, or how about how Aeris died and you couldn't use a Phoenix Down on her in Final Fantasy VII, or how Gwen Stacy broke her spine from physics that were soundly ignored up until that point...
The list goes on, and on, and on. Sometimes little things, if not thought through or poorly executed, can break immersion by not upholding the non-verbal contract of our suspension of disbelief.