Mr. Brunner is Percy's favorite teacher, and teaches Latin. Later, Percy realizes that Mr. Brunner is Chiron, a very smart centaur who has trained many heroes before Percy's time, including Hercules. At Yancy Academy, Chiron helps Percy learn about Ancient Greece (the history of the gods and the Titans). He tells Percy, "what you learn from me […] is vitally important. I expect you to treat it as such. I will accept only the best from you, Percy Jackson" (1.66). Percy describes Mr. Brunner/Chiron for us:
Mr. Brunner was this middle-aged guy in a motorized wheelchair. He had thinning hair and a scruffy beard and a frayed tweed jacket, which always smelled like coffee. You wouldn't think he'd be cool, but he told stories and jokes and let us play games in class. He also had this collection of Roman armor and weapons, so he was the only teacher whose class didn't put me to sleep. (1.14)
On Percy's first day at Camp Half-Blood, he realizes that Mr. Brunner's name is actually Chiron and he has the body of a horse. He helps Mr. D run Camp Half-Blood, training young demi-gods for a life of battling monsters. Chiron tells Percy that he inserted himself at Yancy as a Latin teacher, because he wanted to watch over Percy and because he had a suspicion that Percy was a big deal.
Chiron is very wise. His whole job is to help train demi-gods for the work of a hero. He pushes Percy hard in Latin class and beyond, setting high expectations for him. Chiron is also really good at interpreting the Oracle's prophecies, helping Percy understand his own prophecy.