“Colleges” as divisions within the university came about as students faced problems in getting good housing. Students could arrive for university studies as young as 14 or 15.
Medieval rich people often donated money at death to found some kind of ongoing work that would promise to pray for their souls. Monasteries and chapels were the most obvious targets, but some began endowing boarding houses for university students. Theology was always a portion of the first four years’ study, even if students went on to law or medicine, so it was presumed that these young men would be a very good prayer cohort. The founder might specify that his own descendants be preferred, or he might specify a certain number of students who could not pay their own way. At the Sorbonne, the first college was a boarding house for poor theology students at the University of Paris (which offered only theology).
You can read Chaucer’s description of a student, including his obligation to pray for donors, here.
Endowing a college meant setting up a house with some basic staff: cook and laundress. Then someone had to oversee the selection of residents and make sure they prayed for the founder, so colleges also needed manciples or deans. Students who lived in colleges were better behaved, compared to the students who lived in town and were constantly disorderly. College manciples could evict residents who did not follow rules like chapel attendance and curfew. Universities became more respectable places as the college system developed. By the late Middle Ages, some colleges charged living fees, but many students were still taken on full or partial scholarship. The poorest might have to help serve dinner, but they still had the respect of wealthier boys since they had won their places by competition.
Colleges proliferated and grew into communities of more than a boarding house. To help its students, a college built up a library of common textbooks. Then, to help them more, in addition to their attending university-contracted lectures, a college’s residents could work with tutors hired by the college itself. These tutors lived and taught right there on site.
Before the college housing system, universities had no real buildings. The colleges that grew up around them became the first campuses and gave the university brick and mortar solidity. Colleges also promoted the ideal of a scholarly community. Students who lived in other rooms sometimes became petty thieves, in addition to rioting and setting fires. Colleges turned it around; they provided quiet study halls, libraries, tutors, and common dining as we expect today.
I don’t suppose most of them still pray for the founders’ souls, but let’s hope that those generous souls made it out of purgatory long ago.