Well, many many books existed before movable type was invented in the mid-15th century (in Europe). The important thing to keep in mind is that the enormous effort and cost needed to produce a functional press for the first time could be justified because so many books already existed. Mass production of books depends on a key factor: confidence that you can sell all the copies that are produced. Whereas earlier in the Middle Ages, individual books were created only on demand from a committed buyer already, by the 15th century, bookmakers could expect a market for books they produced.

In the specific case of Cambridge: medieval universities had three advanced faculties: theology, law, and medicine. There was some geographical specialty, such as the Paris being better know for its theologians and Bologna/Italy for their lawyers.

The earliest catalogue for the Cambridge Library dates to 1424, although certainly the uni had library holdings earlier than that. Of the 122 volumes listed, over half were theological in nature. That could mean anything from Augustine to liturgical commentaries to Thomas Aquinas. Certainly Peter Lombard's Sententiae were represented, since commenting on the Sentences was the basic theological task. A good chunk of the remainder were canon and civil law. The balance, probably philosophy (especially Aristotle) and medicine. It's not until a big donation in 1529 that classical literature (Greek, Roman) is well-represented in Cambridge's library.

One important thing to keep in mind is that "122 volumes" does not mean 122 "books" like we would think of today. Some works were so long they would have been held across multiple volumes. Other codices would have held multiple different texts in one.