It could be about his family's hidden vault that he didn't know before. Maybe there are some secrets or powerful magical items left for him by his parents.
The letter might be a warning. In fanfiction, Gringotts could be aware of a dark wizard trying to steal from a vault. So the letter is sent to a character, perhaps Harry Potter himself, to inform him that he needs to protect his vault or help in the investigation. It could also contain some secrets about the security measures of Gringotts that only the receiver can use to safeguard their property.
Well, often Harry could receive financial help from Gringotts in fanfiction. Since he has his parents' inheritance there. The goblins, who are known for their strict business ethics but also a sense of fairness, might provide him with enough gold to buy rare magical items or hire the best tutors to improve his magical skills.
It can start a new quest. If the letter reveals a hidden task, like finding a missing key to a vault, it gives the characters a clear goal to pursue. This drives the plot forward as they search for clues and face various obstacles along the way.
It might make him more aware of his family's past and connections. If the letter reveals something about his family's wealth or status, it could change how others view him.
One possible motive could be to stop Voldemort from getting his hands on some crucial dark magic item stored in Gringotts. Harry might think that by destroying it, he can prevent Voldemort from getting more power.
One possible implication could be that Harry has access to unlimited wealth and resources. This would change his status significantly within the wizarding world. He could use the gold to fund various projects, like improving Hogwarts or helping out the less fortunate wizarding families.
One consequence could be that he unknowingly steals something that has a powerful and dangerous magic attached to it. This could put him in great danger as he may not be able to control or understand the magic. It could also lead to a chain of events that disrupt the balance of the wizarding world, as things from Gringotts often have a long - standing significance and influence.
In some fanfictions, when Harry Potter gets his letter at 9, it might be a moment of great excitement. It could be the start of his journey into the wizarding world just like in the original story, but with some unique twists added by the fanfiction author. Maybe the owl that delivers the letter has some special markings or behaves in an unexpected way.