The first thing we learn about Jess is his ambition to be "the best runner of the fourth and fifth grades" (4.2). And that's what drives him for the first several chapters of the book – being the fastest and best runner. It's something he can improve if he works really hard, that will make people proud of him, that's totally accepted in his society, and that will be seen as masculine – all pretty important things for a kid who feels like a bit of an outcast. But while he might have some ability, Jess just isn't naturally the fastest runner: he has to work really hard at it. When Leslie comes along, she easily beats him and all the others, and for all we know she never trained at it.
Jess's other, more secret ambition is to become a good artist. He has to draw because he can't help it. The encouragement of his teacher Miss Edmunds seems to be counterbalanced by his father's total disapproval. But with Leslie in his life, Jess seems to have enough permission to want to draw and to draw better. As he's talking with his new friend, "he yearned to reach out and capture the quivering life about him [but] when he tried, it slipped past his fingertips, leaving a dry fossil upon the page" (4.111). Leslie's the one who helps him see "the poetry of the trees" (4.111). With her in his life, he's able to fantasize about a career as an artist, and to start to shape a future outside of Lark Creek and beyond his parents' expectations.
Obviously Jess's friendship with Leslie alters him tremendously. For being a mere fifth grader, she really teaches him to be more courageous, more imaginative, and more thoughtful. Because he has her in his life, he can exercise his generosity and become more fully himself. He "need[s] to give her something" (6.6). His friendship with her makes up for the things that are lacking in his family life (6.23), and, just as she would be alienated without him, he would be "lonesome" without her. He's "able to be Leslie's one whole friend in the world as she [i]s his" (7.112).
At first Jess feels like an interloper (an intruder – not someone who runs off to get married) at Terabithia. He thinks he can't even get there without Leslie because it won't feel transformed: "It needed Leslie to make the magic" (7.2). But by the time he goes to the National Gallery with Miss Edmunds, he's starting to see the outside world the way Leslie taught him to see Terabithia: "Entering the gallery was like stepping inside the pine grove [… it was] so obviously a sacred place" (10.53). He's becoming able to see the Terabithian aspects of the ordinary world, to "make the magic" (7.2) for himself.
When Leslie is abruptly taken from him, Jess is completely devastated. He goes through several stages of grief, including blaming her for helping him open his mind like that:
She had tricked him. She had made him leave his old self behind and come into her world, and then before he was really at home in it but too late to go back, she had left him stranded there. (12.17)
And it's true that she did leave him there far too early. There was more she could teach him, and more he could teach her. The world is a lesser place without Leslie in it, but Jess is richer for having known her at all.