I think of magical realism in more simplistic terms, as the example greenbookworm gave. Magical (to the reader) elements that are taken for granted by the characters. Such as the neighbor being a nice guy and oh yeah, he's a centaur so when we go to concerts together, I take the horse trailer.
Well, here's what I think is a pretty good example from an anime I'm currently watching called
Mawaru Penguindrum.
In the anime, there is a place called the "Child Broiler" where children go when they are no longer wanted, abandoned, and want to disappear from this world, where they are then set on a conveyor belt and shredded into pieces to become "invisible".
Now despite some other elements of magic elsewhere in the story (which are irrelevant to this particular example), it's quite clear the story is set in our present-day, urban, realistic world. For the most part (disregarding certain major exceptions for the main characters), the world in the story operates without magic or anything that would be extraordinarily out-of-place in our own world, and functions more or less according the rules and conventions of our reality.
However, according to the rules of our reality (and therefore, the general world of the story), the idea of a physical place such as a "Child Broiler" that shreds unwanted children to pieces so they can become invisible actually existing is ridiculous. No such place exists. However, in the world of the story, it's established as a physical place, that really does exist, in which action takes place.
There is nothing
overtly "magical" about this "Child Broiler." Nonetheless, it's something that would be out of place in our world. In the reality we know, it's not something that would physically exist. However, despite the world in the story for-the-most-part functioning and resembling our own world, it's simply accepted as a part of the world in the story.
Now what is the function of this "Child Broiler"? It's metaphor. It may be representative of an orphanage, a foster home, abusive parents, or simply loneliness and isolation. In a non-magical-realism story, a character might imagine such a place as the "Child Broiler" as a metaphor for how he feels, to describe the extent to which he is in despair, is lonely, and how much he wants to give up. In magical realism story, it's not metaphor. It's what
is. Events and development actually take place there, even though, rationally, its existence makes no more sense in the world of the story than in our own world. Yet because it makes sense metaphorically, emotionally, spiritually, it exists. There is no clear line between metaphor and reality.
The actions that take place between characters in the "Child Broiler" are clearly a metaphor for the internal struggles of accepting oneself and coping with loneliness and abandonment, the struggles of making connections with other people despite feeling completely unwanted by the world, and trying to save others who feel the same way. But because it is a magical realism story, even though it's a metaphor,
these metaphoric events and actions actually take place in the world of the story.
It's a natural consequence of the postmodernist idea that perspective shapes the reality. In magical realism, this idea can become entirely literal. Because sometimes metaphors, analogies, abstractions can be more real than vague and imperfect reality.
So it's not just that your neighbor is a centaur. It's not just that everyone takes it for granted that he's a centaur.
Why is he a centaur? Because despite growing up enjoying the convenience and plenitude of modern life and being spoiled by consumer culture, his family is from the forest. They grew up tilling the earth and living amongst nature. He has not been home since he was born. He has taken in the modern world, become a part of it. But as the weight of consumerism and civilization slowly grow upon his shoulders, and his comfortable life in the city feels increasingly suffocating, he finds himself trapped between the desire to be among the comforts of civilization and all of its accomplishments and to return to nature and find what he might have lost. Struggling to determine the direction of his heart, these thoughts continue pressing on him until one day he wakes up as a centaur, a liminal being caught between the natures of civilized man and the untamed wild, struggling to find his identity.