It could mean several things. Firstly, if 'nymf' is related to the traditional concept of a nymph, it may mean that the fanfiction is giving Bella Swan a more ethereal and nature - bound quality. Maybe she has powers related to nature, like being able to communicate with animals or control plants. It could also be a way to set her apart from her original character in the Twilight series, making her more of a mysterious and otherworldly figure in the fan - created story.
When Bella Swan is called a 'nymf' in fanfiction, it might be a way for the author to re - imagine her character completely. A nymph - like Bella could have different physical characteristics, perhaps more delicate and with an almost supernatural beauty. In terms of her role in the story, she could be a protector of a certain natural realm in the fanfiction world. Or it could be that the 'nymf' description is part of a complex backstory where she was born from or is related to some magical or natural origin that the author has devised, which would be very different from her original human - turned - vampire story in the Twilight saga.