From what we know it only means that "She is coming after him."
But just as in English we can try to imagine why she is doing that and what her intentions are.
- Perhaps she is behind him in some kind of race?
- Maybe he came in first and she is arriving a little bit later?
- It could be about the alphabetical order of their names?
- Or maybe she is following him and if she catch up she intend to kill / kiss / beat / tickle him?