You know the manuscript (or, indeed, the published life-writing or novel) which doesn't grab you, though it all seems very competent? You know the kind of rejection which is the editor or agent saying that it's all very good but no thanks? The thing is, it may be good, but it's all the same kind of good. It's like travelling through a beautiful landscape by driving along a motorway at a steady 50mph in a comfortable car: you see it all, you may even have the windows open to smell the breeze, but you don't experience it bodily: which of course means mentally and emotionally.
"Variety" is an apparently superficial term for what's lacking; the cure apparently an unsatisfactory bolting-on of crudely "different" stuff for the sake of it. But variety matters in writing for really profound reasons. For one thing, the Christmas Rule* applies. And for another, our pattern-making human brains are thickly wired to work in terms of difference and similarity. Keeping the reader convinced and reading is all about finding the new and strange in the familiar, and the familiar in the new and strange. And each time the next bit of familiar (the story, characters, the logic of the next sentence) is de-familiarised by being conveyed in a different way, our minds catch and recreate these things as new.
The classic way to find real variety is to imagine more widely and deeply, and to develop the strength and range of the language in which to express that imagining. But if that hasn't happened naturally it's often possible to work quite cold-bloodedly to bump-start your engine by pushing the car. So here are some things to push at:
Time. You can tell the story of a year in one sentence, or the story of a day in six hundred pages, so decide when your narrative should be real-time or even more expansive (it's Bloomsday, today but it takes longer than a day to read Ulysses), and where you want to compress time and cover the ground, while making your Telling Showy. Will you take the reader on a high-speed magic carpet across time to the next important scene, or will you just jump-cut there? Where might you, within a scene, compress or expand the narrative according to what matters now, or will matter later?
Psychic distance. All narratives work by moving closer into and further out from one or more individual characters' consciousness. But how wide is the range you use? Unless you're very experimental then you're unlikely to spend the whole narrative at one or other of the extremes, but the wider the range you can learn to write, and then exploit, the more energy your storytelling will have. Plunge the reader deep-deep-deep into the physical and mental experience of a character. Pull right out and speak as a storyteller spinning a tale, letting the seeds you've planted in the reader's mind flower in their own particular climate.
Characters: How do they contrast with each other? Can you make more of that? When they interact, how can you exploit their interaction to power the drama of the scene, as well as its tone? How do they think, and speak? How do their voices and their points of view colour the narrative in free indirect style? If a character is your narrator, does that older-and-wiser consciousness contrast with the younger unknowing consciousness of them as an actor in the story?
Settings: We all have our default settings (mine seem to involve food and drink: kitchens and cafés), and it can seem very cold-blooded to decide that one of those café meetings will, instead, happen in a park. And yet, because your characters are always in action in their environment, as soon as you put them in a different setting, they will, perforce, act slightly differently. Even if the emotional moves of the scene are the same, they'll be expressed differently: instead of fiddling with the sugar-jar to avoid his antagonist's eye, your protagonist will be scuffling about in the leaves. And suddenly they come more alive, because we've seen them in a slightly different light.
Sentences. We all have natural patterns and lengths of sentences that we fall into, but if they're all the same our pattern-making brains are lulled into inattention. A narrow range of shapes of sentence also means you're not able to work on the reader in as many ways as you might. It's obvious how short sentences work, on the whole, but it's worth thinking about how long ones work, to develop your sense of the possibilities of both. You could even take a poetry course (taught, or self-taught) as actors do yoga: so their bodies are ready and unrestricted in responding to what the part demands.
Voice. Not just the characters, but the voice of the narrative. How do they contrast in tone, vocabulary, sentence length and syntax, imagery? The stronger and more distinctive the voice and point of view of the narrative, the more effective it will be when the characters' voices and points of view begin to colour it, as we go deeper in in psychic distance. And, as we all know, it's voice that grips readers from the beginning.
Particularity vs. Archetypicality*. As the Showing and Telling post puts it, particulars - "rotting willow" or "sapling oak" - tend to conjure things more vividly for the reader than archetypes such as "big tree". On the other hand sometimes you want to give the reader the plain, monumental minimum, and leave their imaginations to evoke the reality in the space that creates; there's more on this question here.
*not sure that's a dictionary word, but maybe it should be.
Pace. All stories need a rhythm of systole and diastole, because life has one. It's obvious that a fast pace is exciting but it's also realistic when there's lots happening; yet even James Bond washes up on a beach and catches his breath, waits for his wounds to ease, plans his next move. The reader needs that slowing-down too: time to absorb what's happened as one can't while it's happening; time to absorb surroundings, implications, emotions and themes; time to look forward with hope or fear. But readers need the speeding-up too: short and flash fiction because it's so often built round a single incident or consciousness, is particularly inclined to suffer from being too even-paced; and to my mind not enough teachers talk about this problem.
Triumph and Disaster, Hope and Despair. This is about what for want of a better term I'll call variety of direction in your story. Fortunately-unfortunately, in other words. Things go well and hopes lead our eyes upwards, for a sentence, or for a scene, or chapter or act. And then bang: down we plummet in the next sentence, or next scene. Yes, it's vulgar. But then storytelling is.
You can start from externals or internals, macro- or micro-focus, and follow them to the other end of the range. Often I've spotted, say, a run of dull, competent but same-y sentences, which revealed that the way my character was acting was just one damn thing after another, without any change or tension. I've had students who got what I'd tried to explain about a year-in-a-sentence versus Ulysses, and applied it brilliantly to a single, pivotal scene in their story. One of the gorgeous things about writing, as a creative practice, is that anything which makes your story better told doesn't have to have made it better told first try. You can think about variety diagnostically, therapeutically, in revision. It'll make your story more alive than ever.
* The Christmas Rule is that if you want red to be really red, and green to be really green, you put them next to each other. Otherwise known as the Asterix and Obelix Rule.