In the 'Twilight: Rosalie Finds a Baby' fanfiction, the baby's significance could be multi - fold. It could be a way to humanize Rosalie further. As a vampire, she has lost much of her humanity, but taking care of a baby could bring out her more human side. The baby might also be a link to the human world that Rosalie has distanced herself from. It could also be that the baby is a plot device to introduce new conflicts or relationships. For example, if the baby has a family that is searching for it, it could lead to Rosalie having to interact with humans more, which is always a complex situation for vampires in the Twilight series.
Since I haven't read the 'Twilight: Rosalie Finds a Baby' fanfiction, I can only guess at what it might entail. It could be that Rosalie discovers the baby in a dangerous situation, like in the woods near Forks. And then she decides to protect it. It might also explore how her vampire nature interacts with this newfound responsibility of taking care of a baby. Maybe she has to hide it from the other vampires or deal with the baby's family if they're involved.
The baby could be an orphan from a war - torn area that Ruby Rose discovers. It might have no known family, and Ruby's discovery of the baby could be a turning point for her character, making her more empathetic towards the plight of the innocent in such situations.
It's possible that the baby's parents are from a rival pirate crew. In the 'luffy finds a baby fanfiction', this could lead to a lot of drama as Luffy has to decide whether to return the baby to its potentially dangerous family or keep it safe with his own crew. Or perhaps the baby's parents were victims of a powerful and evil force, and Luffy feels compelled to protect the baby from the same fate.
Maybe the baby is a result of some sort of magical experiment gone wrong. And Harry Potter finds it in a hidden place where the experiment was carried out. The baby might have some strange and unpredictable magical abilities as a consequence.
The baby could be an ordinary human baby that has some sort of latent magical ability that Raven senses. She then decides to protect the baby from the human world that may not understand or accept the baby's potential magic, and also from the magical world that might want to exploit the baby.
The baby could be an orphan from a nearby village that has been attacked. Kagome stumbles upon the baby while on her travels with Inuyasha. Since she has a big heart, she can't just leave the baby there, so she takes it with her.
The baby could be a lost elf child from a different part of the forest. Maybe their family was attacked by some dark force and Thranduil finds them by chance.
The baby could be a half - demon, related to some other important character in the series. Maybe it's the offspring of a character Sesshomaru has some history with.
The baby could be the child of a minor character from the original series who was in hiding. For example, the baby might be the offspring of a wizard who was on the run from Voldemort's followers and unfortunately didn't make it, leaving the baby behind for Harry to find.
One idea could be that the baby is from a hidden clan. Naruto decides to protect the baby from those who would use its special abilities. He takes the baby under his wing and trains it as it grows up, passing on his ninja values.