Origins
The word 'university' descends from Latin 'ūniversitās,' which in classical Latin meant 'the whole, the totality, the aggregate.' It is formed from 'ūniversus' (all together, whole), a compound of 'ūni-' (from 'ūnus,' one) and 'versus' (turned), the past participle of 'vertere' (to turn). The literal meaning is 'turned into one' — everything combined into a unity. The PIE root behind 'vertere' is *wert- (to turn), which also gave English 'verse' (a turning of the plow, hence a line of writing), '-ward' (toward, in the direction turned), and 'worth' (that toward which one turns, hence value).
The transformation of 'ūniversitās' from a general word for 'totality' into the specific name for an institution of higher learning is one of the most important semantic shifts in the history of Western education, and it happened in the twelfth century. In medieval Latin, 'ūniversitās' was a legal term meaning 'a corporation, a guild, any body of persons constituted as a legal entity.' There was nothing inherently academic about it. A guild of merchants, a guild of craftsmen, a guild of physicians — any of these could be called a 'ūniversitās.' The full phrase that gave us the modern meaning was 'ūniversitās magistrōrum et scholārium' — the corporation of masters and scholars.
The first institutions to bear this title emerged in Bologna and Paris in the late twelfth century. At Bologna, it was the students who formed the corporation — they hired and paid the professors, set the curriculum, and fined teachers who lectured too long or skipped topics. At Paris, it was the masters (teachers) who constituted the guild, organizing themselves into 'nations' based on geographic origin. In both cases, the 'ūniversitās' was not a building or a campus but a legal entity — a group of people who had banded together for mutual protection and self-governance, just as craft guilds did. The scholars needed protection from rapacious landlords and hostile townspeople; the masters needed protection from the interference of bishops and kings. The corporate charter gave them both.
French Influence
Oxford, Cambridge, and the other universities that followed in the thirteenth and fourteenth centuries adopted the same structure. Gradually, 'ūniversitās' — which had originally referred to the human community of teachers and learners — came to refer also to the physical buildings they occupied and the institution as a whole. By the time the word entered English around 1300 via Old French 'université,' this transfer from people to place was well underway.
The 'uni-' prefix, meaning 'one,' links 'university' to 'universe' (all things turned into one), 'universal' (pertaining to the whole), and 'union' (a joining into one). The '-verse' element connects it to an entirely different family: 'verse' (a line of poetry, from the turning of the plow at the end of a furrow), 'version' (a turning, hence a particular rendering), 'convert' (to turn with), 'reverse' (to turn back), 'diverse' (turned apart, hence varied), 'controversy' (a turning against, hence a dispute), and 'vertigo' (a sensation of turning). Few words in English sit at the intersection of two such productive Latin roots.
The modern university retains something of its medieval corporate character. Academic self-governance, the granting of degrees, the tenure system, and the distinction between 'town and gown' all descend from the twelfth-century moment when a group of teachers and students in Bologna and Paris decided to form a 'ūniversitās' — to turn themselves into one.