Alumni are people who attended a given institution, usually one of learning. In the context of Davis, it most often refers to UC Davis alumni, but it can also mean alumni of other local schools. Periodically you hear the term "alum" to refer to a single person, but the correct word is alumnus, as anybody with education should know.
UC Davis alumni are tracked by the Cal Aggie Alumni Association based out of the Buehler Alumni & Visitors Center. Some are dues-paying (i.e. official) alumni members, but all are tracked and, upon graduation, start receiving UC Davis Magazine and as a courtesy are mailed any specific copy of The California Aggie gratis.
The Cal Aggie Student Alumni Network works to keep an open channel between current students and the alumni.
Also see the list of alumni that have obtained fame after leaving UC Davis.