What's an example of deep? Well, let's take a look at magic. First of all, you've gotta go beyond the trope of wizards in pointy hats with a mysterious source of power. (Or, for that matter, wands with magic words--no more Harry Potter magic, please!). R. Scott Baker's The Prince of Nothing series goes deep with magic. Those who perform magic are called "Schoolmen" because they belong to different "schools" of magic. One school bases its magic on "the analogies," meaning that all their magic looks like something else. (A dragon, a bird, etc). That school is jealous of the closely guarded method of magic of another school, which does not have to use analogies but can get to the "essence" of the magic. Unfortunately, those folks must suffer a disturbing side-effect: every night they dream about the end of the world, as experienced by their founder a thousand years ago. All schoolmen can recognize the "mark" of magic on others, except for one group of enemies. To practice their magic, this group gouges out their own eyes and wraps trained snakes around their neck to see.
It gets more complicated, but you get the idea. Pretty cool, huh? This is so far from wands and crystal balls that any comparison is laughable. Bakker has thought out his world of magic and, by doing do, made it deep. A short story, of course, can't have all of that, but even one piece like that can make it stand out.