When Percy is studying for his Latin exam, he is rather stressed, not only because of the exam but also because he has recently been told that he won't be returning to the academy next year. He is also confused and preoccupied with the mysteriously sudden disappearance of Mrs. Dodds. In this stressed state of mind, the words on the page in front of him seem to do odd things:
Words had started swimming off the page, circling my head, the letters doing one-eighties as if they were riding skateboards.
In this quotation, the words are personified. They are given the capacity to swim "off the page" and perform "one-eighties" on a skateboard, while "circling" Percy's head. Personifying the words in this way makes it easier for the reader to imagine that they have a life of their own, just as we do, and this in turn emphasizes how Percy has lost control of the words. He is no longer active but has become passive. He feels like the world is swirling around him, refusing to follow the basic laws of the universe as he knows them.
Later in the chapter, Percy overhears his friend Grover talking to Mr. Brunner about him. The talk seems ominous and ends with Mr Brunner insisting that they worry only about keeping Percy alive "until next fall." Percy, understandably, becomes anxious and retreats down the hall, where he sees an ominous shadow.
A shadow slid across the lighted glass of Brunner's office door, the shadow of something much taller than my wheelchair-bound teacher, holding something that looked suspiciously like an archer's bow.
In this quotation, the shadow is personified as an archer, seemingly towering ("much taller") over Percy. The shadow is personified simply to suggest that its owner is some sort of conscious being, stalking Percy from the shadows. The "archer's bow" implies that perhaps the owner of the shadow is hunting Percy, which only serves to exacerbate his current confused, anxious state of mind.