Nursery rhymes are traditional little poems for small children. They are an important part of English-language culture because everybody [1] knows about "Mother Hubbard" and "Little Miss Muffet" and "Mary Mary Quite Contrary".
Jack Sprat could eat no fat, His wife could eat no lean, But in between the two of them They licked the platter clean.By the way, I have read that the nursery rhyme "Ashes, Ashes" is based on the Plague in London, and "Jack Sprat" satirizes corruption and venality during some monarch's regime.
In any case, Jack Sprat is often referred to as a shorthand for cooperation between parties whose interests do not conflict, and possibly complement each other.