Edmund, younger brother to Peter and Susan and older brother to Lucy, starts out as—oh, how shall we put this?—a totally despicable jerk.
In the beginning of The Lion, the Witch, and the Wardrobe, Edmund talks back to Susan, defies Peter, makes fun of the kindly Professor, and teases Lucy about her claim that she has traveled to another world. It's suggested that Edmund's experience at school has turned him into a bully.
As Peter says to Edmund:
"You've always liked being beastly to anyone smaller than yourself. We've seen that at school before now." (5.13)
Some of Edmund's unpleasantness also comes from his clash with Peter, and Peter admits to Aslan that his treatment of Edmund might contribute to his brother's attitude.
When Edmund finally does make it to Narnia, he is discovered by the White Witch, who plays on his greed and selfishness. The Witch convinces Edmund that she will make him a prince and give him power and authority.
Foolishly, Edmund consumes enchanted food and drink that the Witch gives him (including two freaking pounds of Turkish delight). The combination of Edmund's own flaws and the Witch's power makes him a traitor to his brother and sisters.
The narrator is careful to explain that Edmund is wicked, but not necessarily evil:
You mustn't think that even now Edmund was quite so bad that he actually wanted his brother and sisters to be turned into stone. He did want Turkish Delight and to be a Prince (and later a King) and to pay Peter out for calling him a beast. As for what the Witch would do with the others, he didn't want her to be particularly nice to them […] but he managed to believe, or to pretend he believed, that she wouldn't do anything very bad to them. (9.3)
Lying to himself, Edmund betrays his siblings to the Witch. In this fantasy story with overtones of Biblical allegory, Edmund is like Judas—the trusted member of the inner circle who turns out to be a traitor.
Of course, as soon as Edmund delivers the information that the Witch wants to hear, she takes him hostage and treats him very badly, forcing him to march across the damp countryside without a coat, cold, wet, and hungry.
During this journey, Edmund has a small revelation when he sees a group of animals enjoying a feast that Father Christmas gave them. The Witch, angry that her anti-Christmas spell is clearly breaking, turns them to stone:
And Edmund for the first time in this story felt sorry for someone besides himself. (11.21)
Edmund's ability to feel sympathy and pity demonstrates that he can be reformed—as the poor animals get turned into statues, Edmund's stony heart becomes more human.
Eventually, the Witch decides to murder Edmund, but he's rescued just in time by Aslan's followers. At this point, Edmund has a long, private conversation with Aslan.
There is no need to tell you (and no one ever heard) what Aslan was saying but it was a conversation which Edmund never forgot. (13.25)
After this experience, Edmund changes radically. He asks his brother and sisters to forgive him, and they do. He becomes a valuable part of Aslan's army, attacking the Witch when everyone else is too frightened to do so and cleverly destroying her magic wand.
Wounded in the battle, Edmund is healed by Lucy. Crowned King of Narnia along with his siblings, he becomes known as King Edmund the Just, "a graver and quieter man than Peter, and great in council and judgment" (17.21).
Edmund's change of heart, not unlike a religious conversion, is the only significant character change that takes place in The Lion, the Witch, and the Wardrobe. If you think about it, all the other characters are constants who don't change or develop. The Witch is always evil. Aslan is always good. Lucy is always truthful. Peter is always brave. And Susan is always gentle.
Sure, the other children may develop a little—Peter discovers reserves of strength and Susan pushes herself beyond her normal limits—but only Edmund goes through a radical transformation. Edmund's journey from nasty traitor to wise judge is the central conceit of the book and shows Aslan's power more than any particular feat of magic.