Jargon Jungle (D)
A higher education qualification of a certain level. They split into undergraduate degrees or first degrees which are usually Bachelorships degrees (masters, doctorates, and various postgraduate PGCEs and so on). A university isn't a university if it doesn't teach degrees although some do other higher education qualifications too like Higher National Diplomas (HNDs).
Most universities break down different subject areas into departments and students 'belong' to whatever department teaches their course. It gets more complicated if they study more than one subject, because they may end up in several departments. Some universities don't have departments, they have schools or faculties instead (or even as well), but they're basically the same thing.
Slang for a lower-second class honours degree, ie, a Desmond Tutu (two-two. Geddit?). For the record, a first is known as 'a Geoff' (Hurst), a 2.i is 'an Attila' (the Hun) and a third is 'a turd'. Don't blame Push if you get a third — we didn't invent the rules of Cocker-nee rhyming slang.
The Department for Education and Skills
Dons are Mafia bosses, but in the context of universities, particularly Oxbridge, they're more likely to be lecturers, tutors or other academics who do teaching.