The difference between a character driven story and a plot driven story (correct me if I'm wrong), is that in a character driven story the character(s) wants something badly enough to go after it. I much prefer these stories to the alternative, so I'm going to list a few popular examples and discuss them with as few spoilers as possible.
Max, in WHERE THE WILD THINGS ARE, longs for adventure, something a little more "wild." Then, when he's had his adventure, he longs "to be where someone loved him best of all." His desires are easy to relate to, especially for his target audience; Sendak's picture book is a classic.
Maltilda longs for a family that will love and understand her, and she longs to learn. I adore all of Roald Dahl's books, but MATILDA is the easiest for me to relate to (though if your longings lean more towards a life-long supply of chocolate or turning evil witches into mice, that's alright by me).
In TWILIGHT, Bella longs for Edward and everything that he stands for: ageless beauty, immortality, power, and, in her mind at least, perfection. This is harder for me to relate to because, unlike Bella, I don't see Edward's perfection. But I can understand the appeal: perfection is a worthy goal.
Now that we've talked about character motivations, what do you long for? That's a rather personal question, and I don't expect you to answer (unless you're longing to). But do your longings always motivate you? I know that mine don't. Some of them are counter-productive. For instance, my babies have all been born allergic to chocolate. They grow out of it, but I can't eat chocolate when I'm nursing without seriously distressing my them. Unfortunately, I long to eat chocolate. I dream about eating chocolate. I have nightmares about eating chocolate and causing my babies to projectile vomit. Do I act on this longing? I do not. On the other hand, I love my children and long to have common points of interest with them. I read to them. I play sports with them. I garden with them. I sing with them and encourage them to practice musical instruments. I pray with them, take them to church with them, and explain what's most important to me and why. This is a longing I can and should act upon, but, if I were to force what is important to me on them, that longing would also be counter-productive. I have found that longing tends to lead to obsession, which can be good or bad. Obsession is a driving force. Like Matilda, I long for learning. I longed for a college degree, and I have one. I long for publication as a sort of validation or justification for the time that I spend writing, but, even more than that, I long for time to write. However, I also longed for a family very much like the one I've been blessed with, and I long to spend more time with them. I also long for more sleep. I find my longings at odds with each other, struggling for priority.
Whatever our longings may be, they influence our decisions. One of the most powerful examples in literature is in THE TALE OF DESPEREAUX, by Kate DiCamillo.
I do not cry easily, but there are two parts in this book that get me every time. I'm tearing up just thinking about them. The first part has little to do with this post, but when the princess asks Miggery Sow what she wants, that has everything to do with it. Dang. I'm crying. If you haven't read this book, you should read it. If you have, feel free to guess the other part that made me cry.