In fantasy literature, a hedge wizard or hedge magician is a wizard of low ability, generally self-taught or with a low education background as opposed to the common examples of being apprenticed to a mentor or studying though a structured educational system. Some fictional backgrounds identify them more with rural than urban backgrounds. In novels, many uses of the term are derogatory, describing a character as incompetent, uneducated, of lower social standing or of lesser power. It is similar to calling someone a hack or slob but specific to practitioners of magic.
In role-playing games and video games a hedge wizard is usually a weaker wizard encountered when still at a lower level. With a limited number of spells and lacking in power they are normally easy to defeat.
In the Discworld books, the term 'hedge wizard' is used to describe a wizard who specializes in the magical properties of plants. Although this does fit with the idea of a more rural wizard, it is likely to be a deliberate pun on the word 'hedge'. As it is written in the novels: "If you invited a hedge wizard to a party he'd spend half the evening talking to your potted plant...and he'd spend the other half listening to it."