Art

When a professor asks you to "cite your sources", what's the point? 

Well, citations serve three major roles in scholarly work:

1. They allow you to show how your argument is built upon the ideas of others.
2. They allow you to indicate which ideas are taken from others, and from whom those ideas were taken; in other words, to give credit where it's due.
3. They allow the interested reader to follow your argument and confirm its logic by investigating the ideas on which the argument is built, or to further explore those ideas on their own.

In each case, it's important that you acknowledge the ways in which others' ideas contributed to your own. Otherwise, you run the risk of plagiarism.
If you incorporate or refer to others' theories, words, ideas or concepts in your paper, you must document each one using a citation.