The thing about growing up with Fred and George,"said Ginny thoughtfully, "is that you sort of start thinking anything's possible if you've got enough nerve.

This quote means that when you grow up with two brothers like Fred and George, you come to believe that you can do anything as long as you are brave enough to try. Ginny is saying that her brothers have encouraged her to believe that she can do anything if she sets her mind to it and has the courage to go through with it.