In case you haven't read the book, Anne Frank was an outspoken, talkative and optimistic person; Margot Frank was a very shy and quiet person.
They're both hiding in the annex so that the Nazis don't find them and send them to concentration camps. The relationship between them is that they are sisters. I'm not sure what they disagree on, I read the book long ago. But Margot was much more mature than Anne, so it was probably something about that.