The grad. committee is responsible for determining program and graduation requirements for all CSE graduate students. This includes cognates requirements and degree requirements. It also handles admissions and final approval of assistantships (TAships, RAships, etc.).
Attend meetings, offer students viewpoint when necessary, participate in discussions about the program requirements. You will also need to help Dawn organize the prospective student visit in the spring. This mostly involves asking for volunteers to go to dinner and handling a few of the logistics of the dinner.
Once a month in the Fall, once a week in the Spring, though the CSE rep doesn't have to be there for all of the Spring meetings as most of it is just admission decisions.
Traditionally, the CSE rep also coordinates taking vising prospective students out to eat with current graduate students. This usually just involves finding a few other grad. students and arranging a time and place to meet, and answering the prospective students' questions during that time.