I'm sure you're familiar with the metaphor. Ogres are like onions because they have layers. Simple enough.
But really, the world is full of onions. People are layered. Objects are layered with meaning. Language is layered. They're all like onions.
So what has this got to do with writing?
Come back to people. People are layered. We enjoy reading because we like it when the characters surprise us. Their minds work in ways that we don't see. I hear often enough that characters are not real people. While this is most certainly true, while characters are subjective creatures of the author's narcissistic whatever, I find it helps to pretend they are real. You need to plant them, the little onion seeds of your characters in your fictional onion-layered world, with a brownish French onion sky, and you need to pretend these characters are real within your world and they are layered with characteristics and personalities that even you haven't met yet.
I find this separates the good stuff from the bad stuff, not just in novels and short stories, but in films and in TV shows. I get sick of Mr Predictable Action hero guy because he's superficial, he's filled with shit. He's butter through and through, he's spread thin with sameness and blandness.
I recently read American Gods, by Neil Gaiman, which takes place in a god-infested America with so many archetypal gods it could have been so easy to go 'herp derp zeus throw lightning hurr', but rather it moulded these most basic of characters and ground them so deep into his world that their layers ran much deeper than our expectations.
I've recently warmed to the idea of the 'nested narrative' setting stories inside stories to comment on the original story, to mutate it, to change its meaning, to give it layers.
I think it's always good to show a few layers of a story, the characters, the layers of the narrative, and while it may be as simple as questioning the nobility of your protagonist, and while you don't need to peel through every layer that defines your character and defines your story, I think it's essential to always have something else going on, some layers to give your stories depth.