A peculiar and painful fad in literal-minded Ankh-Morpork.
The reasoning runs: phrenology insists there is an inter-relationship between the outer shape of a person's skull, and those areas of the brain lying directly underneath. Thus, if there is a noticeable bump in the front of the skull, this is directly over the area of the brain thought responsible for intellect and should be evidence for an abnormal amount of brain development and activity directly underneath - ie, the intellectual personality.
Ankh-Morpork takes this a step further. What if a series of carefully measured blows on the head with carefully graded hammers could adjust the shape of the skull, thus modifying personality accordingly? Unfortunately, the leading practitioner is Zorgo the Retro Phrenologist, a troll, to whom sublety is one of dem word fings in dat dict-ee-o-nary fing.
You can go into a shop in Ankh-Morpork and order an artistic temperament with a tendency to introspection. What you actually get is hit on the head with a large hammer, but it keeps the money in circulation and gives people something to do.
Phrenology developed in the Victorian era and is closely bound up with the related pseudoscience of craniometry developed by the Italian Cesare Lombroso: Lombroso thought that a criminal type could be identified by precise measurements of facial and skull features and the ratios between them. The leading practitioner of this art on the Discworld was Captain Findthee Swing of the old Cable Street Particulars
There is also the Monty Python sketch about taking "being hit on the head" lessons, where people pay to be bashed over the skull...