He had become what Ajihad wanted: an authority independent of any king or leader. (59.14)
In some ways, you can argue that this is the climax of the novel. Sure, it was cool when Eragon killed Durza, but his journey to maturity really comes to a close with this realization. He has at last become his own man, able to stand on his own. As he realizes in this moment of reflection, Eragon has truly become a Dragon Rider.