In Discworld, Granny Weatherwax discusses "headology" fairly often as one of the keys to her power. What exactly does she mean by the term?
Like psychology, but many witches think "psychology" is a bad word, or that it means "having a psychological problem". The practice of headology relies on the principle that what people believe is what is real. This is used by witches to earn respect or at least fear, and also to cure patients.
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Basically, headology is applied psychology, although mistress Weatherwax would never describe it in those terms.
Headology is akin to psychology, but based within a world where people's fears often manifest themselves physically. It also seems to function as a catch-all for the terms 'reverse psychology', 'placebo effect' and with a fair amount of 'stagecraft' thrown in for good measure:
Granny Weatherwax had never heard of psychiatry and would have had no truck with it even if she had. There are some arts too black even for a witch. She practiced headology—practiced, in fact, until she was very good at it. And though there may be some superficial similarities between a psychiatrist and a headologist, there is a huge practical difference. A psychiatrist, dealing with a man who fears he is being followed by a large and terrible monster, will endeavor to convince him that monsters don’t exist. Granny Weatherwax would simply give him a chair to stand on and a very heavy stick. - Maskerade
“It seems to me,” Magrat tried again, “that the only magic we do is all—well, headology. Not what anyone else would call magic. It’s just glaring at people and tricking them. Taking advantage of their gullibility. It wasn’t what I expected when I set out to become a witch—” - Witches Abroad
“So people see you coming in the hat and the cloak and they know you’re a witch and that’s why your magic works?” said Esk.
“That’s right,” said Granny. “It’s called headology.” She tapped her silver hair, which was drawn into a tight bun that could crack rocks.
“But it’s not real!” Esk protested. “That’s not magic, it’s—it’s—”
“Listen,” said Granny, “If you give someone a bottle of red jollop for their wind it may work, right, but if you want it to work for sure then you let their mind make it work for them. Tell ’em it’s moonbeams bottled in fairy wine or something. Mumble over it a bit. It’s the same with cursing.” - Equal Rites
Headology is more or less "Applied Psychology." In other words, where psychology is the study of the mind, Headology is the practical application of psychology.
In the discworld, where narrative is a literal force of nature, peoples' perceptions of the world can have a profound effect on the world itself. This means that proficient practitioners of Headology, such as Granny Weatherwax, can have an immense power on the world around them through the people who believe what they present.
An example of this power is perfectly demonstrated in the book Witches Abroad, where Granny Weatherwax uses headology on Mrs. Golgol; in the book, Mrs. Golgol used the power of her voodoo doll to cause pain to Granny. Granny's response was to tell Mrs. Golgol to watch closely. Once Mrs. Golgol was watching, Granny stuck her hand in the flame of a torch. This caused the doll to burst aflame.
What happened was that Granny was using Mrs. Golgol's belief against her. Mrs. Golgol believed that anything done to the doll would affect Granny instead (and because of this belief, it worked). So, Granny used that belief to reverse the effect; if what happens to the doll can affect Granny (without hurting the doll), then it's also true that what happens to Granny could affect the doll (without hurting Granny).
In essence, Granny didn't use a scrap of magic, she simply used Mrs. Golgol's own power by manipulating her thoughts and perceptions.
Well, it's like magic, but instead of arcane knowledge, you use common sense. At least that is my understanding.