Magic "is the basis for all power. The language describes the true nature of things, not the superficial aspects that everyone sees" (19.50).
Two things we learned from this Brom gem:
(1) Holy crap.
(2) Magic is a language.
We'll focus on the second part. Magic and language are completely intertwined. Brom tells Eragon, "if you wish to employ the power, you must utter the word or phrase of the ancient language that describes your intent" (20.22). In order to become a proficient magic user, then, Eragon must learn the "true" language of the world around him. This kind of powerful insight is required if he's going to be able manipulate reality. So it's not just about reading a bunch of hocus pocus out of a spell book, it's about crafting a true understanding of reality. Deep.
In this way, Eragon's development as a magic user is a symbol of his growth as a person. As he matures, his magical power grows, but so does his understanding and acceptance of the world. He's more cautious about wielding his power, since he's better able to process the consequences and has a better grasp of reality. Oddly, that grasp of reality comes by studying magic—but magic is a reality in the world of Eragon.