Graduate programs typically have a faculty committee that oversees admissions decisions. Some admissions committees also include graduate students, but many do not.
Often applications of students interested in a specific research area are reviewed by faculty in the corresponding research area. Decisions might be made by those faculty or by the committee as a whole. Decisions may depend on contingencies such as current funding or faculty capacity to take on new graduate students, as well as the merit of individual applications and how well they match the research interests of the faculty.