Death is "a catastrophe." What kind of catastrophe? A distant, quiet one. Distant and quiet are adjectives referring to "a catastrophe."
"Distant" means far away. It can mean in far away in TIME, or PLACE, or even someone's thoughts. For example: "I do't care about her. She is only a distant thought."
In this case, the authors (Freakonomics, right?) are saying that people don't think about heart attacks every day, because a heart attack is something that isn't happening now. It's distant in time. It might happen some day far in the future.