In monastic orders, one of the set prayer times involves the monks getting out of bed at four in the morning for a service of sacred song, prayer, and meditation.
At Unseen University, the equivalent is a mealtime unknown anywhere else in creation: at around four in the morning, the tables are set for Somnambulistic Nibbles. As the name implies, this might have at least begun as a service to wizards who not only sleepwalk, but sleep-eat.
We are assured in The Science of Discworld III: Darwin's Watch that being asleep is no longer an entry requirement to the Old Refectory for any wizard feeling a little bit peckish at this hour of the day, and who cannot stand the long wait for Early Breakfast at six o'clock in the morning. It is entirely possible that this is a service much appreciated by Ponder Stibbons and other wizards pulling all-nighters in the High Energy Magic Building who find themselves in need of essential sustenance.
While not mentioned as such in Unseen Academicals, this is the time of the night where the Night Kitchen is of supreme importance, Glenda Sugarbean becomes one of the most important people in the University, and in fact a lot of the fine detail, dialogue and argument of the book must be played out over this mealtime.