What does Scout mean: ''I know now what he was trying to do, but Atticus was only a man. It would take a woman to do that kind of work.''

This quote, at the very end of Chapter 13, follows a very awkward conversation between Atticus and Scout.  Aunt Alexandra is in town, and basically impresses upon her younger brother to talk to Scout (in particular) about being a lady.  He never actually uses these words - but as he attempts to quote Aunt Alexandra it is clear that this is what she means.

Scout herself has no idea what Atticus is talking about.  He uses Aunt Alexandra's words, "Not run-of-the-mill people," and "product of several generations' gentle breeding."  It is clear Atticus himself doesn't buy into it, and cannot sell the idea to Scout that she should be acting lady-like, wearing dresses, learning manners, preparing to be a debutant one day, etc.

In fact, Scout doesn't understand it until much later (as she tells the story from an adult perspective) that it was impossible for Atticus to guide Scout to becoming a young woman "of society."  It was really a mother's job and it would take such a mother to role model it first and teach it that way.