Perhaps Harry discovers that Snape had a much deeper connection to his mother than he initially thought. Snape's love for Lily Potter could be explored in more detail, showing that his actions towards Harry were influenced by his feelings for Lily. This could involve Snape secretly protecting Harry in ways that were not obvious in the original story.
At first, Harry probably sees Snape as a cruel and unfair teacher. But as he learns the truth, he starts to view Snape as a hero. He realizes that Snape was on his side all along, despite the way he treated him.
It could be Hermione. She is always so smart and observant. She might have stumbled upon some hidden information and decided it was time for Harry to know the truth.
Well, in such a fanfiction, Harry might learn some hidden secrets about his family. Maybe he discovers some long - lost relatives or some dark secrets about his parents that were previously unknown.
He might be extremely shocked. Snape has his own views on the Malfoy family and Harry Potter. Given his complex relationship with both, he could initially be in disbelief and then perhaps a bit angry that Harry would be a fan of a Malfoy.
Another truth could be related to the wizarding world's history. Harry might learn that there are secrets about the founding of Hogwarts that have been kept from him. For example, he could discover that one of the founders had a connection to a powerful magical artifact that is now lost. This knowledge would change his perspective on the school he loves and his place in the wizarding world.
It could be that Snape teams up with Harry to solve a mystery that is crucial to the wizarding world. During their cooperation, Snape shows his loyalty and intelligence. He may sacrifice some of his own interests for the greater good. Harry witnesses all these and realizes that Snape is not the person he thought he was, thus learning to trust him.
Well, in many 'Naruto learns the truth' fanfictions, it could be about Naruto finally learning the truth behind his parents' death. Maybe he discovers some long - hidden secrets about the Uchiha clan that were concealed from him all along.
His loyalty becomes more evident. In the original story, his loyalty to Dumbledore was somewhat hidden under his grumpy exterior. In this fanfiction, as Harry is learning to trust him, Snape's loyalty to the side of good and his care for Harry become more pronounced. He might take more risks to protect Harry and Hogwarts, and his actions are no longer so easily misinterpreted as malevolent.
Snape is likely to be initially suspicious. He has long held a rather negative view of Harry, so when he discovers Harry is good at potions, he might think Harry has some ulterior motives or has received improper help. After all, in the regular Hogwarts setting, their relationship is quite tense.