What does Dickens say has to be understood before the story of A Christmas Carol can be of any significance?   

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shakespeareguru eNotes educator| Certified Educator

Right in the first four paragraphs of the story is the answer to your question.  It is the fact that:

Marley was dead.. . .Old Marley was as dead as a door-nail.. . .There is no doubt that Marley was dead. This must be distinctly understood, or nothing wonderful can come of the story I am going to relate.

Dickens stresses that this must be understood just as, in the play Hamlet, it must be understood that Hamlet's father is dead.  The appearance of a ghost who relays what life is like "on the other side," makes its appearance and subsequent request of the living person (be it Hamlet or Scrooge), and this appearance is a life-changing event.

Marley's Ghost will come from beyond the grave to warn Scrooge of the terrible torments that await him if he does not mend his ways.  He will send three Spirits to assist Scrooge in understanding why and how to change.  Scrooge must believe all of these things if he is to save his own soul before it is too late.

So, Dickens wants to assure the audience that it is their ability (and Scrooge's) to believe in Marley's Ghost that creates the environment for his (and the audience's?) amazing change of heart.