If anything from my experience of the last 15 years or so has made itself clear to me as a story truism, it's that the importance of the smallest details matter.
The difference between a dull scene or stock character and one that breathes, that thinks, is in the details. Details spring out and suggest themselves when the story artist believes in a character's reality no matter how superficially unlikely the scenario they're placed in might be.
There are times when a story artist is given a sequence that's already laid out pretty extensively: the characters must say this or that, do this, that and the other thing, get from here to there. You might think that that would be a boring sort of sequence to work on. Not necessarily.
Of course one wants to be as creative as one can, but in putting a feature film together there's not always an opportunity to start from scratch(and if there always is, the film's probably in trouble). Does that mean there's no room for the story guy to have fun, to make an impression, to enhance or "create" the scene? Far from it. But you'd better believe in the characters you're working with.
If you do, wonderful things can happen. Some of it might wander off in a direction that will result in the kibosh being put on the sequence in whole or in part--a great big old redo. But sometimes (often enough if you're both lucky and inspired) a sudden, truthful idea will pop up out of nowhere and work so well it's just got to go in. No one planned for it until it struck--you didn't see it until you were least expecting it, surrounded at your desk by crumpled paper and worn down stubs. Suddenly it's there, and it seems exactly the thing the character should say or do at that moment. If it really is as right as it feels, it'll make it into the film. You'd be surprised how often that happens in spite of any and all obstacles.
This to me is the most exciting, rewarding part of my job, but it's not a daily occurrence--it couldn't be. Films just don't play with too much going on at every second, all the time. They flow in a narrative dance in any of a million permutations, all with one commonly understood goal: to tell you a story.
And I should mention that the function of your storyboards is twofold: not only are you designing the action within the frame, but most importantly you're responsible for setting the mood and emotion of the scene--that's how it's supposed to be, anyway. This really can't be stressed too strongly. The times that a completely flat, emotionless story sequence didn't work in boards but came to life in animation, out of nowhere, is exactly zero. Can sequences be plussed by animation? You bet, and they almost always are--hugely. The medium is about moving drawings/characters, after all. But plussing has to start from something. The drawings needn't necessarily be fancy, but they must certainly read and communicate.
We in animation have a big hurdle, a doozy: we have to take a two-dimensional, stylized design of a character and entice the audience into caring about it. I believe the key to doing that is to lend the characters your faith while you board them--to invest them with little parts of your life in the form of those little details.
All of this comes from you, from your own real, personal experience and your unique observations. To have to squeeze the wonky story-peg into a predetermined hole doesn't always work. Often these characters take over, just a bit. Or a bit more than a bit. To know when and how to apply your observation and build each character a soul--that's where your day to day story experience hopefully takes you.
It's why I do this job, why I love it. It's like climbing a mountain that grows as I grow. The mountain is impossibly huge, but it can be conquered at the most unpredictable times if you keep your imagination open and remember to mine truth from the little details of life.