A university is where sims in your city can go to for further education in their young adult lives. Like its real-life counterpart, the university consists of a campus, with various educational buildings on the school grounds.
The university in SimCity 3000 is a reward building, which helps improve the overall E.Q. of your sims. It is only unlocked after the average E.Q. exceeds 105. Like with other reward buildings, the university will raise land value in the surrounding area, for residential and commercial development alike.
A university is a job-providing reward building in SimCity 4, which can be acquired through meeting the requirements of unlocking the building, or simply completing a UDI mission; because of this, only one university is allowed per city (without the use of external cheats). Not surprisingly, the university is the largest educational facility available ingame, and like the city college, it doesn't have a educational radius, unlike other educational facilities, such as elementary schools, or high schools. Also, like the city college, school buses are not unlocked by the university, and do not spawn around either of these buildings.
A university is not required to have a well-rounded educational system, although building one will help educate sims further, as well as improve your mayor rating. Note that it is also an extremely expensive option, coming out at 1,500 simoleons each month.