Back in The Lion, the Witch, and the Wardrobe, Peter was Peter the Magnificent, "High King over all Kings in Narnia, Emperor of the Lone Islands and Lord of Cair Paravel, Knight of the Most Noble Order of the Lion" and blah, blah, blah (13.12). Yeesh, no wonder this guy gets others to address his letters for him. But at the start of Prince Caspian, Peter's just another schoolboy on his way to fall term.
Does this mean the Peter of Earth and the Peter of Narnia are two different people? Not at all. In fact, it's not Peter's titles or what he wins that makes him the hero of Prince Caspian. It's his personality—specifically his courage and chivalry—that position him as the true hero of the tale, maybe (maybe!) even more so that Caspian himself.
Like the Christian knights of medieval romances, Peter is a role model of courage and chivalry. Although a dated concept today, chivalry was the code that the knights-errant lived their lives by. It included virtues like honor, gallantry, courtesy, generosity, valor, humility, and devotion to one's god. Yeah, that's a pretty hefty list. Oh, and it sometimes includes not fighting unless it's absolutely necessary.
Sound like Peter? Yeah, we'd say so.
When Peter is dueling Miraz, he knocks the evil king down to the ground. But instead of finishing him off, Peter, "[steps] back, waiting for him to rise" (14.35). Even Edmund wonders if Peter makes the right move here, but then remembers that such "'gentlemanly'" behavior comes with "'being a Knight and a High King'" (14.36). Even in a life and death situation, Peter stands by his chivalric principles and refuses to slay a man on the ground (or with glasses—can't hit a man with glasses).
Peter's courage is shown to us in the duel itself. He thinks up the idea when he realizes the Old Narnians are totally outnumbered by Miraz's forces. He chooses to duel the king in order to "prevent the effusion of blood" and "[avoid] all other inconveniences likely to grow from the wars now levied in our realm of Narnia" (13.14). In other words, to prevent more people and lives from being destroyed, Peter will shoulder the responsibility of the war himself and do the fighting. That's pretty courageous, yes. But what makes it really awe-inspiring is that Peter has no idea if he can win or not. As he tells Edmund, he's "'fighting [Miraz] to find out'" (13.82).
And guess what Peter gets for fighting on Caspian's side? In a word, nothing.
That's right. Peter doesn't receive land or titles or treasure for helping Caspian battle Miraz. He enters the fray because it is the right thing to do. And to make it even more impressive, Peter could have the throne and all the treasure he could possibly want if he chose. He is the High King, after all, and the rule of Narnia belongs to him by right. But instead, as he reassures Caspian, "'I haven't come to take your place, you know, but to put you into it'" (12.77).
To serve and not take, that's the way of the knight. And that's Peter Pevensie. Modern day knight and school boy rolled into one.