During the High Middle Ages, universities arose in Europe. These medieval universities were unlike anything that had existed in Ancient Greece or Rome. They played an important role in both intellectual and political life during this time.
Universities played an important role in government and in society. By the High Middle Ages, governments were becoming more complex and legalistic. Governments were no longer just run on the whim of an individual lord. Instead, there were laws to be interpreted and applied. There were taxes to be imposed and collected. Governments needed educated people who could do these things and who could generally administer government functions. The universities were important because they were the institutions that turned out the educated people who could do these things. They also turned out people like teachers and doctors who were important to society as a whole.
Intellectually, universities were very important as well. The universities were the first institutions of learning that tried to be independent of both the church and the secular authorities. Universities started out as guilds of students and teachers created to protect the rights and the interests of these groups. One of the things they tried to do was to allow for some amount of academic freedom. In other words, they tried to create a space in which scholars could think independently, rather than having to conform to what the church or a secular ruler wanted. This was an important step in the intellectual world. Universities created a new space for academic freedom and for the institutionalized passing on of knowledge on a relatively large scale.
Thus, universities were important both on the intellectual level and on the more tangible, societal level.