This quote comes at the end of the story, when Montag has escaped the clutches of the mechanical hound and is with Granger and his group of book people. Granger tells Montag about his grandfather, and how he used to tell Granger about his worries that civilisation had forgotten about nature and how wonderful and dangerous it could be. Let us examine what his grandfather said in context:
"'I hate a Roman named Status Quo!' he said to me. 'Stuff your eyes with wonder,' he said, 'live as if you'd drop dead in ten seconds. See the world. It's more fantastic than any dream made or paid for in factories. Ask no guarantees, ask for no security, there never was such an animal. And if there were, it would be related to the great sloth which hangs upside down in a tree all day every day, sleeping its life away.'"
Status Quo is a Latin phrase meaning "the current state of affairs." To keep the status quo is to keep things as they are and not to change them. Granger's grandfather is making a joke, treating status quo as if it were a Roman name, but also making a serious point about how we as humans should always be open to change and new experiences, and truly living.