It could be a sign of an unexpected alliance. Maybe Harry realizes that Snape has some hidden motives that are actually for the good, and the basilisk parts are a valuable resource that can help Snape in his own quests, like for potions or in dealing with certain dark magic threats.
Perhaps it's a form of apology or reparation. Harry might have discovered that he misjudged Snape all along. The basilisk parts are very powerful and rare, so giving them to Snape could be his way of making amends for all the times he doubted or antagonized him.
Perhaps Harry has a hunch that Snape is involved in some secret project or fight against the dark forces that requires basilisk parts. Harry, being the hero he is, decides to provide Snape with the parts to aid in this unspoken cause. It could also be a sign of Harry's growing maturity and his ability to see beyond their past differences.
He might be initially suspicious. Snape is a cautious man, and he may think that Harry has some ulterior motive, like setting him up. But after realizing Harry's sincerity, he could be grudgingly grateful.
They could also be used in some form of dark magic defense. Snape might use the basilisk parts to create spells or enchantments that can protect Hogwarts from dark creatures or dark wizards. Maybe he could create a magical barrier using the basilisk parts' power that repels any dark magic approaching the school.
The significance could be about character development. It might be a turning point for Harry and Draco to start seeing each other in a new light.
It could signify a turning point in their relationship. They've had a rocky relationship in the original series, so this could be a moment of reconciliation. Snape might finally be seeing Harry as more than just James Potter's son.
It could be a sign of forgiveness. Snape's will might be a way to force Harry, who represents the side of good, to reach out to Lucius, who has been on the wrong side. By giving something to Lucius, Harry is showing that there is a chance for redemption even for someone like Lucius.
It could be a turning point in their relationship. Maybe Snape starts to see Harry as more than just James Potter's son. The scars represent Harry's battles and traumas, and seeing them might make Snape more empathetic.
Another way Snape could comfort Harry is by standing up for him in certain situations. Maybe when other teachers or students are being unfair to Harry, Snape steps in and defends him. This act of protection can be a great source of comfort for Harry, as it shows that someone is on his side even if they have had a rocky relationship in the past.
In some fanfictions, Snape might use his advanced knowledge of potions to brew a special healing elixir for Harry. He could also use his magic skills, like a complex spell specifically designed to mend Harry's wounds, whether they are physical or emotional.
The significance could be that it's a way to rewrite their relationship. In the original story, they have a lot of tension, but in fanfiction, this act of spoon - feeding can show Snape in a more nurturing role towards Harry, which is a big contrast to his usual harsh demeanor.