The night circus revolves around time. The book skips around through time. Also time plays a huge role in the circus it goes by but it is extremely slow and you barely notice aging.
This clock represents time and the role it plays in the novel. The novel is told in a non chronological order which represents the absurdity of time. In truth, time, in the novel as well as real life, is simply a man-made illusion and truly means noting unless one decides it does.