A story is a confluence of many aspects. Think of a recipe: when you create a delicious one, there are many ingredients that go into making it.
Grammar, scenes, plot, characters, twists, prose, dialogue, tension, themes, beginning, middle, end, plot devices, similes and metaphors, just to name a few, all go into the recipe of making a good story, and depending on what you use too much of or lack therein, the end result may or may not turn out the way you expected. That's why it's so important to read a lot, because then you can pick apart what other authors use in their recipes, and you can learn what is most effective. Then you can study more on the different aspects and add them in your stories. It's not a science, but it is a learned thing, and it's only by writing a lot and reading even more that you can achieve potentially brilliant results.
The other way I often look at storytelling is like a layer-cake, or a dessert called a mille-crèpes (a stack of crepes with creamy filling between each one. Maybe some fruit. Chocolate. Blog writing always gets me hungry!). The reason why this is so is that each layer adds to the yumminess of the whole. Perhaps you should go eat now and come back later for the rest of the article. Go get a snack and come back. Serious! Go!
Anyhow, the more crèpes you have, the more immense and filling your dessert. If you decide to concentrate on plot and some grammar, you might have a cohesive story, but not something considered filling by any metric.
Here's my other point: When you look at a mille-crèpe from the top, all you see is the top-most layer (naturally). In a story, that layer would be your grammar and voice, as well as your prose, say. It's the visible part, that which pops out and catches the eye.
What is hidden underneath, however, is everything else, and in my mind, every subsequent layer is the deeper stuff, the things that become more and more intangible the more crèpes you remove. Are you taking a bite of your snack every time I say "crèpe"? I know I want to. If you have a second and haven't already, google mille-crèpes. They're so good. Plus you'll get the visuals of what I'm trying to tell you. You know what? Never mind. I'm going to put that up as the image for this blog post. That way people will start salivating as soon as they see it. Am I evil or what? There are a million different varieties. Go check them out.
So, the deeper you go, the more involved it gets in the actual storyline, but the less you see of it. The plot, plot twists, plot devices, would be the second layer, say. You follow the plot along while reading the first layer (grammar, voice, prose). You dig a little deeper and you'll find the characters, and their story arcs, as well as the amount of fleshing out and back-story they received.
Further down, next level, you can get more in depth and even less obvious. The tension, the pacing, etc.
And to me, the last layer (are there only five layers? Hey, it's only a metaphor. You can see a hundred layers if it make you happy), are the themes explored.
This, to me, is one of the most important layers of a book, and one of the most easily overlooked. No matter what you write about, there will be a theme. Whether you're exploring it consciously or unconsciously is entirely up to you. Like all aspects of writing, there are limitless amounts of themes. There are universal themes and very narrow ones, and everything in between. The theme you pick (or not) somewhat defines how "important" your work might be considered (with, of course, all the other layers added in). Just to give you a few examples, Charles Dickens explored the themes of extreme poverty. J.K. Rowling explored the themes of friendship and love, and unifying to fight evil. Stefanie Meyer's themes were the importance of having a boyfriend.
In the end, you decide whether you want to explore a theme consciously, or just "let it happen". The theme will be there anyway, whether you like it or not. It's a dilution of your thoughts on a particular subject, and will always end up in your writing. What separates a lot of great writers from merely good ones, though, is the way in which they approach their themes, and their timelessness in respect to the whole of humanity as a community and its search for commonality.
All stories, whether written in a book, in a video game or on the silver screen have themes, overt and covert. What will yours be?