According to Liza, what “began her real education”?

From the text:

LIZA [continuing] It was just like learning to dance in the fashionable way: there was nothing more than that in it. But do you know what began my real education?
PICKERING. What?
LIZA [stopping her work for a moment] Your calling me Miss Doolittle that day when I first came to Wimpole Street. That was the beginning of self-respect for me. [She resumes her stitching]. And there were a hundred little things you never noticed, because they came naturally to you. Things about standing up and taking off your hat and opening doors—