This being a book about knights, we figured swords would get mentioned somewhere. And we were right! As in, mentioned on practically everywhere. In page school, swords are a pretty big deal. Alanna's not even allowed to begin training with a sword until her second year, and even then, she doesn't begin to learn how to use a sword until she can make one herself. Talk about being thorough.
Having to make your own sword seems like a good way to impress upon the elite warriors of Tortall that they need to understand where their power comes from before they wield it—and you're probably going to treat your weapon a little better if you had to make it yourself. (Plus, we bet wielding a blacksmith's hammer gives you some pretty sweet muscles.)
Even after that whole rigmarole, Alanna freaks out about learning to fight with a sword:
It was like taking any other test, only ten times worse. A knight lived or died by his swordsmanship. Without a mastery of swordplay, she would be no knight, have no adventures. (5.191)
Just she fears, Alanna is defeated pretty quickly at her first swordfight. But does she give up? Not our girl. Instead, she borrows Coram's sword in order to practice with it at night, reasoning that if she can learn to yield a sword that almost outweighs her, she'll be able to wield anything. Here, the borrowed sword symbolizes Alanna's stubbornness and ambition: large and perhaps a bit unwieldy.
But when Alanna retrieves a magical sword from Sir Myles of Olau's ruins—on that almost kills her—it takes on a new meaning: as soon as she accepts that she's powerless to stop her own death, the jewel in the sword's hilt flashes to life and she's released from the death-spell.
Back at the capital, Lightning serves as a stand-in for Alanna's own magic, which she's been trying to conceal from Duke Roger. When he sees the sword, he kind of freaks out: "Duke Roger's voice was quivering with—what? Rage? Impatience? Fear? Alanna wasn't sure" (6.230). He acts twitchy and threatened around the blade, and then tries to cover up when he notices the other boys in the room noticing him acting odd. Once again, Alanna plays dumb and insists that she doesn't know what the sword is really capable of, a clear parallel for the way Alanna is trying to get Duke Roger to think of her and her own magic abilities.
To sum up, swords are Serious Business for knights and knights-to-be. As Alanna learns to use a sword, she's also learning about herself—what she's capable of, as well as how it's important to protect herself from unwanted attention.