It can be argued that the overriding conflict in The Magician's Nephew is man versus self. In the story, Digory is pitted against two formidable adversaries, one who is human (Uncle Andrew) and the other, a queen from another dimension, Jadis. However, the reality is that Digory must overcome defects in his own character before he can claim victory over his enemies.
In the story, Uncle Andrew is a small-time magician, whose seeming ambition is life is to discover the secrets of hidden worlds. To do this, he cruelly tricks Polly (Digory's neighbor) into using a magical yellow ring to enter another dimension. Since Polly does not have a way to return to the earthly realm, Digory must go in after her with two green rings. The green rings are the only way anyone can return to earth again after venturing into another dimension.
In their adventures, Digory and Polly discover an enchanted wood that is a portal to other dimensions. Polly dubs this forest The Wood Between The Worlds. Both children have to contend with challenges as they travel between dimensions. By a twist of fate, however, Jadis (the wicked queen of Charn) ends up on earth and makes Uncle Andrew her slave. Although Jadis draws Uncle Andrew's focused attention away from Polly and Digory, the two children must still figure out a way to lure Jadis back to her world.
Digory is especially motivated to do this because he has a sick mother, whom he loves very much; furthermore, he does not want Jadis to enslave the whole world. By working together, both children are able to get Jadis back to the Wood Between The Worlds. There, they try to teleport back into Charn. Instead, Polly, Digory, Jadis, and Uncle Andrew end up in Narnia.
Narnia is an important destination because this is where all the main characters of the story meet Aslan, Narnia's creator. As the most powerful character in the story, Aslan is able to neutralize Jadis's power easily. As for Digory, he must put aside his previously self-seeking nature in order to save Narnia. Since the witch was never supposed to enter Narnia, Digory must help Aslan keep the witch out.
To do so, Digory must travel to the west of Narnia to retrieve an apple from a magical tree. He is to bring this apple back to Aslan without delay. At the tree, the witch tries to tempt Digory into forsaking his promise to Aslan. She tells him that he should bring the apple back to his own mother, rather than to Aslan. Digory ignores Jadis and runs away. Back at Narnia, Aslan instructs Digory to throw the fruit toward a river. Eventually, a tree grows from the apple, and it is fruit from this tree that heals Digory's mother. Aslan explains that, had Digory succumbed to Jadis's temptations at the tree in West Narnia, his mother would have had to endure an everlasting life of pain and sickness.
So, by overcoming his inclinations, Digory is able to triumph over his adversaries, to save his mother, and to introduce a new generation of children to Narnia (in the other stories).