Final answer:
Horatio is asked by Hamlet to survive and tell the story of the deaths to serve as a warning against plotting and revenge, fulfilling Shakespeare's method of relaying the play's message to the audience.
Step-by-step explanation:
In the final scene of Hamlet, Horatio proposes to tell the story of the series of deaths as a warning against plotting and revenge. After the tragic ending, where nearly all the main characters die, including Hamlet himself, Horatio is urged to survive in order to truthfully explain what has transpired at Elsinore.
According to Hamlet's request, Horatio's task is to ensure that the true events are known, preventing misunderstandings and preserving the memory of Hamlet. This action aligns with Shakespeare's tendency to use characters within plays to relay the moral or message to the audience, as seen in the example of Romeo and Juliet, where the play ends with the need to deliver the moral of the story.