First off, props to Vonnegut for one of the oddest titles on the bookshelf. A Tale of Two Cities is about two cities—London and Paris to be precise. The Great Gatsby is about a guy named Gatsby who is pretty awesome, nay, great.
But Cat's Cradle? How do you write a novel revolving around a child's string game?
By making the game an important symbol, of course. When Newt Hoenikker was a boy, his father, Dr. Hoenikker, tried to play cat's cradle with him. The event terrified Newt, but the cat's cradle becomes an important lesson for his adult self. As he puts it:
No wonder kids grow up crazy. A cat's cradle is nothing but a bunch of X's between somebody's hands, and little kids look and look and look at all those X's….[And] No damn cat, and no damn cradle. (74.28-30)
As the story progresses, Newt refers to the cat's cradle when confronted with the lies people tell themselves to help themselves feel better. John discovers Angela hides her marital problems by pretending to be happy, and Newt answers, "See the cat? See the cradle?" (80.32). It's the exact same response he has to Bokononism.
The cat's cradle is an important symbol for the novel's exploration of truth and lies. Some characters lie to themselves for happiness, like a child pretending to see the cat and the cradle because they enjoy the game. Others can only see the Xs made of string because that's the truth of the matter—but that might just make them crazy.
When considered with the epigraph (Check out our "Epigraph" section!), the title creates a parallel between the book and the children's game. Just like the cat's cradle, this story isn't a true thing. It's a bunch words put together pretending to be something else. The question is: will you be one of the people who accept and find truth in the lie or will you shrug the story off as just another bit of fiction?