“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).
When Chaucer described a student at Oxford, he included the fact that this scholar was under constant obligation to pray for his benefactors. https://chaucer.fas.harvard.edu/pages/general-prologue-0
A CLERK ther was of Oxenford also,
There was also a CLERK (scholar) from Oxford,
286 That unto logyk hadde longe ygo.
Who long before had begun the study of logic.
287 As leene was his hors as is a rake,
His horse was as lean as is a rake,
288 And he nas nat right fat, I undertake,
And he was not very fat, I affirm,
289 But looked holwe, and therto sobrely.
But looked emaciated, and moreover abstemious.
290 Ful thredbare was his overeste courtepy,
His short overcoat was very threadbare,
291 For he hadde geten hym yet no benefice,
For he had not yet obtained an ecclesiastical living,
292 Ne was so worldly for to have office.
Nor was he worldly enough to take secular employment.
293 For hym was levere have at his beddes heed
For he would rather have at the head of his bed
294 Twenty bookes, clad in blak or reed,
Twenty books, bound in black or red,
295 Of Aristotle and his philosophie
Of Aristotle and his philosophy
296 Than robes riche, or fithele, or gay sautrie.
Than rich robes, or a fiddle, or an elegant psaltery.
297 But al be that he was a philosophre,
But even though he was a philosopher,
298 Yet hadde he but litel gold in cofre;
Nevertheless he had but little gold in his strongbox;
299 But al that he myghte of his freendes hente,
But all that he could get from his friends,
300 On bookes and on lernynge he it spente,
He spent on books and on learning,
301 And bisily gan for the soules preye
And diligently did pray for the souls
302 Of hem that yaf hym wherwith to scoleye.
Of those who gave him the wherewithal to attend the schools.
303 Of studie took he moost cure and moost heede.
He took most care and paid most heed to study.
304 Noght o word spak he moore than was neede,
He spoke not one word more than was needed,
305 And that was seyd in forme and reverence,
And that was said with due formality and respect,
306 And short and quyk and ful of hy sentence;
And short and lively and full of elevated content;
307 Sownynge in moral vertu was his speche,
His speech was consonant with moral virtue,
308 And gladly wolde he lerne and gladly teche.
And gladly would he learn and gladly teach.
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.