In the anime and manga series "Death Note," the rule about the maximum time between writing a name and the cause of death is significant because it adds a sense of urgency and suspense to the story. This rule limits the user's ability to control the circumstances surrounding the victim's death, making the use of the Death Note more challenging and unpredictable. It also adds strategic elements to the plot as characters must carefully plan out the timing of their actions when using the Death Note.