Glaives are used to store (and somehow manipulate) septima powers. Lumen was Joule's septima in the Azure Striker Gunvolt. What he meant in this conversation is that originally, the power of the muse belonged to Mytyl, but his father cutoff her septima power. Sumeragi wanted that power, but normal Glaives didn't work. So they created a living Glaive by the name of Joule.