Well, for most situations here, it's because City/State police are underfunded and understaffed and cannot meet the needs of a small city like a University in a timely manor. The law enforcement officers for a University typically train the same as city police and abide by the same/similar governing regulations.

For a campus that may have 30,000-50,000 people on it at any given time, you do need to be able to have quick responses when an incident does occur. The campus police at my local university actually do more than a typical police department might -- sending out txt messages to all students when there is an incident or threat, update details frequently, Help Call Boxes in the parking lot for at night, etc. They even handle situations when a student pulls the alarm during finals week (something that an outside police department would not be able to rapidly respond to and would get annoyed with quickly).

Some universities even have their own fire departments. Most have medical staff on duty for students as well. Some even have dentists and optometrists, etc. They really are "small cities".