Discordium is both a magical substance or energy (think mana) and grammar. I know that doesn't make much sense, but I feel like that's how magic should be.
The first magicians in the modern sense (i.e., in the sense of the game) were theologians of the Church of the Perfect Light whose studies of the holy texts provided them with what they called "echoes" of the language used to create the world. They realized that these echoes had patterns and rules like those of mundane grammar. When apprehending this fact -- but only momentarily, because they could not hold the apprehension in their minds very long --, they spontaneously generated what they later learned to call discordium. How this apprehension happens and why it is impossible to prolong it remain great mysteries.
Anyway, with discordium the theologians discovered they could manipulate and distort the patterns of creation to make magic. They called it discordium because it was, in musical terms, discordant with the music of creation and the nature of reality. Magic owes its extraordinary effects to this fact.
In-game description of discordium:
Discordium is an invisible but definite substance as well as the grammar of a language -- a concept very hard to wrap one's mind around, but there it is. All magicians use discordium when casting spells, but the process of isolating and preserving it for complicated magical purposes like implement use and ceremonies can be quite challenging. Despite the efforts of some entrepreneurial magicians, discordium, unlike most things, resists commodification.
In less fluffy terms, the "High Magic" trait allows magicians to gather discordium and to use it to power their wands and to trigger powerful out-of-battle spells.