This line is spoken by Faber when he and Montag are talking at his house. The basic idea of the line is that books act to keep us from doing stupid things.
In this passage, Faber is referring to the idea that when Roman emperors had parades, someone supposedly always rode alongside them telling them that they, too, were mortal. The idea was to not let them think they were gods just because the crowds were cheering for them.
Faber is saying that books can act like that for people. Books can make them realize that they don't know everything and that they are liable to make mistakes.
Montag feels like he is missing something from his life. He feels empty. After seeing a woman kill herself for her books, meeting a strange girl named Clarisse, and wondering about his empty life and marriage, he figures that what he needs can be found in books. When he speaks with the former English professor about this, Faber tells him that only some of what he needs can be found in books. Faber argues that not all the answers to what Montag seeks are in books. Books can provide guidance and insight, though. Faber teaches him the following:
"The books are to remind us what asses and fools we are. They're Caesar's praetorian guard, whispering as the parade roars down the avenue, 'Remember, Caesar, thou art mortal.' Most of us can't rush around, talk to everyone, know all the cities of the world, we haven't time, money or that many friends. The things you're looking for, Montag, are in the world, but the only way the average chap will ever see ninety-nine per cent of them is in a book" (86).
As explained by Faber, books can function like a checks and balances system for the fragile human mind. For example, when people become prideful and feel powerful, they can remember stories about characters who might have behaved the same way, then people can choose to learn from the story rather than suffer the same tragic fate. This allusion to Caesar is a way to drive home the point that it is better to remember the stories of others who have fallen and not to make the same mistakes. Also, Faber says that books can bring the world's experiences and knowledge of other places home because a person can't afford to travel the world for that insight--nor can one travel back in time to learn about Caesar and other historical figures.