What does that mean "audit this course"?

Auditing a class means you take a class without getting a grade or credit for a course.

Explanation:

the significance of the title, "the passing", is related to the fact that the main characters, who are three african-american descendant women, are passing as white. this means that, because of their light-coloured skins they look like white women. one of the three friends, clare, is married to a white man and she lives in a white community and she has never told her husband that she is black. the title can easily be connected to the idea of pretending to be someone you are not and of losing your real identity in order to be accepted by society.