The basic answer: any questions you have that weren't able to be addressed in class. The advanced answer: any questions you could not find an answer to on your own.

A large part of studying history is constantly looking for answers to the questions you have - which is how "real" history is done. No one wakes up one day and decides to write a book. They read, form questions, look for answers in secondary sources, and if they have an original idea or find a new source spend years researching and writing in hopes that they will be able to publish.

In the above your professor is a secondary source. Instead of approaching him/her and asking "what/why", ask for reading suggestions on the topic. Then, when you read that book and find an answer, you can check citations and learn where they sourced their information.