Peter is the oldest of the four children who travel to Narnia in The Lion, the Witch, and the Wardrobe. As the oldest, he is the natural leader, notable for his bravery and good judgment.
But he's not 100% awesome—even though he certainly thinks he is.
Peter has high standards, which sometimes make him seem kind of self-righteous to his more flawed little brother, Edmund. Also, sometimes Peter can be blinded by his own self-importance, like when he finds it difficult to believe his little sister Lucy's story about a world called Narnia, even though he knows that she never lies.
Still, in general, Peter is upright and virtuous. When he learns that Mr. Tumnus the Faun has been arrested for protecting his sister Lucy, Peter immediately thinks that it is his duty to try and rescue Mr. Tumnus in return.
During his stay in Narnia, Peter's bravery and leadership skills only increase. When he and his sisters first meet Aslan, Peter takes the lead, speaking to Aslan first when everyone else is too overawed to say anything. Peter also takes responsibility for his failings: he admits to Aslan, without being asked, that his treatment of Edmund may have contributed to Edmund's betrayal:
"That was partly my fault, Aslan. I was angry with him and I think that helped him to go wrong." (12.19)
As Peter's destiny unfolds, he learns that he is to be High King over his brothers and sisters at the castle of Cair Paravel.
In his first swordfight, Peter slays the wolf Fenris, earning the title "Sir Peter Fenris-bane" from Aslan. But Peter's bravery and success don't mean that he feels no fear. On the contrary, when Peter first sees Fenris attacking Susan, he:
[...] did not feel very brave; indeed, he felt he was going to be sick. But that made no difference to what he had to do. (12.31)
Peter's bravery consists, not in how he feels, but in how he acts. In spite of his fears, Peter pulls himself together and fights. Similarly, when Aslan leaves him in charge of the battle against the Witch, Peter rises to the occasion.
Although we learn that Peter feels "uncomfortable" about fighting the battle alone, and "the news that Aslan might not be there had come as a great shock to him," he still takes on the task and ends up fighting with the Witch in hand-to-hand combat (14.12).
And we think that's a pretty baller move.
Peter seems to know instinctively how to be a warrior—after receiving his sword from Father Christmas, he needs no training before slaying Fenris and fighting in the battle. He also instinctively begins to think like a military tactician; when Aslan leads his followers to the Fords of Beruna, Peter suggests that they camp on the far side of the river to protect them from a night attack by the Witch.
Aslan tells him this is unnecessary, but that:
"All the same it was well though of. That is how a soldier ought to think." (14.11)
Yup. Peter has what it takes.
But still, we think that Peter's transformation from "English schoolboy" to "High King Peter the Magnificent" in little more than a blink of an eye is one of the more unrealistic aspects of the story.And yes—we know this story has mermaids and talking beavers.
Maybe part of the reason we find Peter's development hard to believe is that it happens more between the lines than that of any of the other children. The narrator delves into Edmund's and Lucy's thoughts quite a lot, and we understand how their attitudes change, but we don't focus on Peter that much.
During the final chapters of the story, the narrator chooses to follow Susan, Lucy, and Aslan, leaving Peter and Edmund "offstage" to begin the battle against the Witch. In fact, the book doesn't really narrate much of the battle—just the very end, when the Witch is killed and Good triumphs over Evil.