The enhanced fencing foils with which Agatha and Gilfend off✣ the attack by Slaver wasps aboard Castle Wulfenbach -- sort of. They're important for three reasons. First, of course, they do keep Agatha and Gil alive, which counts for something. Second, they show Gil a little more about Agatha's qualifications as a Spark, and also give Agatha a chance to show a bit of Heterodyning, the humming that's Agatha's way of getting into the Sparky hyper-focus mode. Third, and important from a narrative perspective, by drawing power from the Heterodyne Device, they provide a hint that the Device is going to be something worth keeping an eye on in the future.
An odd (and, when fighting for one's life with an improvised weapon, irrelevant) side effect of using these swords is that the users briefly appear and disappear in flashes of blue light. This is commented upon by numerous observers, and foreshadows the use of the Heterodyne Device as to allow Gil to escape✣ from his father's solders and rejoin✣ Theo and Sleipnir.