The rule regarding lifespan extension in the Death Note is significant because it introduces a moral dilemma for the user of the Death Note. By sacrificing half of their remaining lifespan, the user can trade for the Shinigami Eyes, which allow them to see others' names and lifespans just by looking at them. This rule forces the user to weigh the potential benefits of gaining this power against the consequences of shortening their own life. It adds complexity and depth to the story by exploring themes of sacrifice, power, and morality.