I'm currently participating in the “Professors for the Future” (PFTF) program at UC Davis for the 2013-14 academic year (more about that here). PFTF is a year-long competitive fellowship program designed to recognize and develop the leadership skills of grad students and postdocs - I was selected after a nomination and application process. The program is pretty intense, and involves all these things: 1) biweekly meetings focused on careers and professional development, 2) A discussion seminar course on "Ethics and Professional Integrity", 3) a "Seminar on College Teaching" course, 4) spring and fall program retreats, and 5) individual projects (read about my project here).
At our fall retreat, Jeff Gibeling (our Dean of Graduate Studies) gave us a great rundown on University Administration. This was extremely useful, and helped clarify all those various titles you always hear being thrown around (vice-chancellor, provost, dean, chair, etc.). In short, the structure of any given university can be summed up by this neat little diagram:
The Board (or Regents in the UC system) is at the top of the administrative hierarchy. Board members are not usually academics, but rather entrepreneurs, businessmen, or people who have political connections (here are the UC system board members). They are selected by the governor for 12-year terms, and these appointments are approved by the academic senate.
The President or Chancellor is one step below, representing the administrative head of a university. The name of this position can be confusing - in the UC system, the President is the system-wide administrative head of all the UCs, while the Chancellor is the administrative head of one UC campus. Other universities may have both positions (President and Chancellor) that serve different functions.
The Provost is the Chancellor's second-in-command, and the chief academic officer of the university.
The right-hand side of the above diagram can be considered the "Executive Branch" of a university, encompassing all the Vice Chancellor and Vice/Associate Provost positions. The name and number of these positions varies across universities, and they may or may not be filled by faculty members (it varies according to the job duties of the specific position).
Below the Provost we come to the Colleges, Schools, and Departments. Departments are the most fundamental structure of a university, groups of Departments together form a School or College. [Note that in at UC Davis, a "School" offers only graduate and professional training, while a "College" offers both undergraduate and graduate training.] Each School/College is headed by a Dean, and each Department in the School/College is headed by a Chair (who reports to their respective school/college Dean). Department Chairs are senior (usually tenured) faculty members: they may be promoted to this position from the pool of faculty members in a department, or occasionally brought in as an external hire. Chairs are in charge of organizing committees, managing departmental budgets, managing the tenure review process, and overseeing the hiring new faculty members.
The left-hand side of the above diagram, the Academic (Faculty) Senate, can be considered the "Legislative Branch" of a university. The Senate is the pool of all junior and senior faculty members from different departments, who are organized into lots of different committees (each with its own chair) and act as a governing body. This is where all your academic "service" obligations come in. Apparently UC Davis has about 30 different committees focused on various issues: the Graduate Council, the Undergraduate Council, Research Committee, Tenure and Promotion Committee, Courses Committee, Academic Freedom Committee, and yes, even a "Committee on Committees" (which appoints members and chairs to other committees).
Finally worth pointing out are Graduate Groups - these are specific, interdisciplinary graduate programs that draw faculty members from different departments. The UC Davis Graduate Group in Ecology, as an example, represents 24 different departments on campus!
This is just a quick (and hopefully useful) overview based on the organization of the UC System, and UC Davis in particular. There can be a lot of variability in administrative structure. However, some things are pretty consistent: for example, you'll always find a Vice Chancellor for Research and a Vice Chancellor for Student Affairs.