She might change the course of events in the past. For example, she could prevent some tragedies that happened to her family. Maybe she would use her advanced knowledge to help her father, Tony Stark, earlier in his life, which could potentially lead to a different future for the Avengers and the whole world.
One possibility is that Tony could prevent some of the major disasters that occurred in the Marvel Universe. For example, he might stop Loki from getting the Tesseract in the first Avengers movie. This would change the entire timeline and prevent the destruction of New York City that followed. Another thing is that he could meet his parents at a different time, which would be an extremely emotional encounter for him. He might also be able to use his advanced knowledge to help Howard Stark with some of his early inventions, potentially accelerating the technological progress of that era.
She could change many important events. Maybe she would prevent some tragedies from happening in the Star Wars universe. For example, she might be able to save some Jedi who were killed during Order 66.
Well, if Robb Stark went back in time, he might be able to prevent his own mistakes and change the course of history. Maybe he could save his family and allies from the tragedies that befell them.
Well, he could potentially change a lot of things. Maybe he would prevent some of the tragedies that happened in the original timeline. For example, he might stop the Uchiha massacre. He could also use his knowledge of future events and the power of the Juubi to make the ninja world a more peaceful place from the start.
Well, in such a fanfiction, the characters might try to change past events. For example, Naruto could prevent some of the early tragedies in his village. Maybe he'd stop the Nine - Tails attack by somehow convincing his father not to sacrifice himself. This would change the whole future of the village and the relationships between characters.
In fanfiction, if Harry goes back in time to the god, he might gain some extraordinary powers. Maybe the god would bestow upon him the ability to control magic in ways he never could before. It could also lead to him changing the course of history, for better or worse.
He might change the outcome of some crucial events. For example, he could prevent the Red Wedding from happening, saving his family and allies. This would completely rewrite the story's future, leading to a different power structure in Westeros.
He could end up altering the entire history of the Gem war. Steven might try to find a way to end the war peacefully much earlier. He could convince the Diamonds to change their ways before things got as bad as they did in the original timeline. This would mean that many Gems who were corrupted in the original story might not be corrupted at all. And the Earth would probably be a very different place, with a more harmonious relationship between the Gems and humans.
Well, he could change a lot of things. Maybe he'd prevent some of the big battles or save some characters who died. For example, he might stop Frieza from destroying Planet Vegeta earlier. It would be a whole new timeline with different outcomes.
In this kind of fanfiction, Edward might try to change the past events that led to his and his brother's misfortunes. Maybe he'd prevent the failed human transmutation in the first place, saving Alphonse from losing his body.