The word 'University' is derived from the Latin word for guild. The church established schools with the purpose of educating people in a particular profession (a non-trade profession), and then universities arose purely for higher education. In the Middle Ages, it was mostly churches or courts who had the better book collections of the times, so therefore those involved with these institutions (who were mostly those with lots of money) therefore had access to higher education. The first university, Al-Azhar, was founded in Cairo, Egypt in 970BC, which was followed up with more being founded predominently in Italy, France, England and Spain (during the 1100s) and later in Germany and Austria (1300s). They had various faculties, as they do today.
In the SCA, a University can be a branch of the society and is referred to as a college. Universities are popular recruitment bases for the Shire/Barony in which the College lies. An Tir has the kingdom wide University of Ithra.
Note that the use of the word University is reserved in New Zealand for actual government acredited institutions approved to use that name, and therefore the Kingdom of Lochac does not use the word University to describe any of its internal institutions.