A lot of the confusion that comes up in talking about the history of universities is that the alternative that existed are typically ignored. So it looks like when one says, "the university was created in the 12th century" that one is saying that educational institutions didn't exist before then. Which is incorrect.

What is a university? The term, from the Latin universitas, means something like a labor union or guild. It means that it was an educational institution that had a charter from a local (usually secular) authority which gave them some degree of political autonomy. It meant, in essence, that these were independent institutions of education. The University of Bologna is the first entity of this character, and was a center for the teaching of Roman Law. Its students were primarily foreigners and had no protection within the city of the Bologna. These students organized themselves into guilds which were meant to protect the rights of the teachers and the students, and regulated what the teaching was meant to be, including the duties and costs of the masters. The masters had their own guild which regulated the awarding of degrees. The other medieval universities that emerged around this time (like Paris and Oxford) had similar sorts of trajectories but different circumstances relating to both their secular and religious political arrangements.

These were not the first educational institutions in Europe, much less the rest of the world! At that time in Europe educational was mostly dominated by monastic schools (initially open to anyone who wanted a religious education, later restricted to monks) and urban schools (cathedral schools for the learning of secular Roman knowledge). The university system ended up displacing these other forms of education, in part because of their connection to the (then new) Scholasticism, with a renewed interest in Latin translations, Aristotle, and other kinds of knowledge that were quite different from monastic or Church educations. And though their relationship with the Church and their states was often fraught, they were given much more autonomy than people were in the rest of these societies and these other forms of education. It's that autonomy that makes a university a university, more so than the education itself — universities are meant to be special places where people can think about things that might not be acceptable in normal society.

Note that I have said nothing about research — and that's important! Universities were not sites of research. That came much later. They were sites for education. And this is what makes them quite different than the Library of Alexandria and the House of Wisdom, for example, both of which were sites of research more so than education. The House of Wisdom was more like a research laboratory than a classroom; you go there once you have acquired skills from some other source (e.g., a madras). I am not an expert on the Academy but my sense is that these sorts of places were much smaller-scale than a university and were more like paid tutorships, a different sort of system entirely. Again, universities did not invent the idea of education. They were just a different model for education, one that was in part a reaction to the fractured political circumstances of medieval Europe.

Universities did not really emerge as sites dedicated to research until much more recently than most people realize. The modern research university — in which research is considered the major activity of the university, with teaching paying for it and training future researchers — dates only to the 19th century (the Humboldtian reforms). Prior to that universities had a much-deserved reputation as a place where research went to die; Galileo could not wait to get out of the university system and into a place where he could spend his time researching and writing as opposed to teaching the sons of merchants and future clergy.

Anyway, the above simplifies a LOT of complicated institutions and changing history but I hope it gives a little more clarity about what we mean by the creation of universities. I find this is interesting to discuss with students who take universities for granted when they are really quite strange institutions. On the history of universities there is a multi-volume set of books — fairly dry but full of useful information — on A History of the University in Europe which goes into the details at great length.