Admissions committees are looking for strong evidence of research potential; that's what your web site should give. At a minimum, your academic web site should have
- Your academic CV
- A list of publications and research projects, with download links.
You may want to include a copy of your research statement, but only if you don't tailor your statement to each department you apply to.
Keep it simple. If your site looks too flashy, you may give the impression that you spend too much time fiddling with your web pages instead of doing research. (Cough.)
Make sure everything that you post on your web site is polished and professional. Proper spelling, grammar, notation, and technical language counts, just as it does in your research statement.
Finally, @aeismail is correct: Do not assume that admissions committees will look at your site; some will, some won't. Your application must stand alone. But if you mention any publications, independent projects, or other results in your statement, point the reader to your site. Even if nobody actually visits your site, your willingness to display your work in public will work to your advantage.