1) It shows you did work.
Any research paper, article, website, study, etc. that shows citations, in any form, appears more authoritative and knowledgable.
2) It makes you look better.
References to other studies show your response to another person's ideas, and show that you considered different points of view on a topic. References also show how your writing contributes to the literature - agree or disagree with another author, offer a new interpretation, inflate your own ego, etc.
3) It makes you think about your own sources.
Do you really think you should cite www.randysbabynames.com in a paper about the American Civil War?
4) It is polite.
It allows readers to know where you get such crazy ideas. It also gives credit where credit is due. After all, you would want someone to give you praise for writing such a marvelous paper.
5) It is fun for the reader (professor).
Most professors have to publish articles as part of their job. It gives them great joy to think other people are reading their work and responding to it. Good or bad responses do not matter. What matters is that they are publishing, but I digress. Consequently, they require citations from student papers. It really tickles them if you respond to an article or book written by someone they know.
6) Fear of plagiarism.
Most colleges and universities have all sorts of scary punishments for students (and faculty) who do not cite their sources.