What does it mean when a girl says you'll be my big brother later?

This means that your age is greater than her, and you give the girls feel is the kind of big brother, when she has difficulties, you step in to help her, so she said that you are her big brother, of course, there is another possibility, that is, you give her a feeling of great maturity, so this girl is so that this girl is also indirectly shows that this girl is insecure, so you need to protect her, and now happened to meet you, and you protect her, so that both of you close the distance. And now it happens to meet you, and you protect her, so that the two of you close the distance.