What can a university student body do?

You don't mean the student body, which is the entire group of students at a university. You mean a student organization. Basically, they can bring to the students the kinds of activities and experiences that those students won't get in the clroom, whether it is bringing in speakers, organizing field trips to labs where interesting things are being done, helping them negotiate the job market, etc. They can also help the university bring in new students by participating in recruiting events. And they can give awards, scholarships, and the like to students and to professors who have been particularly helpful.