Eskarina Smith, who first appeared in the novel Equal Rites, was born in the smithy of the village of Bad Ass in the Ramtops. She is the daughter of Gordo Smith, the local blacksmith. Traditionally smiths have a connection to magic handling iron and fire as they do. To add to this, Eskarina is the eighth child of an eighth child. Drum Billet, a wizard from Unseen University thinks that she is the eighth son of an eighth son and therefore a wizard so he travels to the Ramtops to leave his staff to her. As a child, she shows great magical potential, turning her brothers into animals and defeating a pack of wild wolves. She is trained to become a witch by Granny Weatherwax ( her first student) until it becomes clear that she had Wizards' magic, not Witches' magic. She travels to Unseen University to become a wizard. Unseen University only accepts males as wizard students, believing that females should stick to being witches so she is not accepted and initially takes a job as a servant. There she meets a young self-taught wizard named Simon, He gives lectures on the nature of magic to the senior faculty staff in his first year! Such power inevitably causes ripples in the space-time continuum; the Things from the Dungeon Dimensions, being Thaumivores, creatures that feed on magic, cluster in his shadows, their characteristic chitering noises unnoticed by all... except Esk who is developing her own magical talent. Simon's skills unintentionally open portals to the Dungeon Dimensions, through which the Things attempt to enter. Eventually they burst through and drag Simon off to the Dungeon Dimensions. Eskarina follows to rescue him. She manages this by not using magic, the only way because using magic would only make the Things stronger. She defeats them and returns to Unseen University with Simon where they set up a research group and create a system of the non-use of magic. Both gain an immense and intricate understanding of the workings of time and space. Eskarina is the first and—as far as is known—only female student ever accepted or at least allowed to enter Unseen University.
Eskarina vanishes from the Discworld series for a long time. Despite the Sourcerer's pledge to the Librarian to restore everything "as good as old", she is presumed dead perhaps another casualty killed in the collapse of the Tower of Art, during the battle with the Sourcerer.
As Granny Weatherwax's first-ever pupil, her legend takes on mythical proportions among Lancre's student witches, aided by older witches' attitudes such as Nanny Ogg's "least-said, soonest-mended", Miss Tick changing the subject, or a general "Don't ask" attitude on the part of the older witches.
Later in life, she settled down in the Unreal Estate and returned to being a witch, and begins going by the name of Miss Smith. Esk returns in the fourth Tiffany Aching book, I Shall Wear Midnight. In that novel, Mrs Proust tells Tiffany that a hard-to-find lady (who'd find her with ease) would be keen to talk to her, and that this woman would be well worth listening to. When the Cunning Man is bearing down on Tiffany in Ankh-Morpork, the mysterious "Miss Smith" comes to her rescue, leading her to a safehouse within the Unreal Estate. Tiffany realises who Miss Smith rally is upon seeing Esk's staff; it is currently being used in a Shamble, and Esk has taken the knob off the end, an obvious sexual reference that alludes to her returning to the witches' fold from being a wizard. She looks old, with white hair and wrinkles, but also young, with a ponytail and a childish laugh. She has learnt to manipulate time and space via the Travelling Now. Chatting over tea, Esk dispenses advice to Tiffany and tells her how she walked through time to see the creation of the Cunning Man, over 1000 years previously. Esk says that she has bad memories of her wizarding past - the scary recollections are never a problem, but the "good ones can be difficult to deal with". Miss Smith uses the Travelling Now to contact Tiffany several more times in the novel. Most interestingly, Esk passed on the secret of time-travel to the young Tiffany who, at a climactic scene in the book, is aided by her older self.
In a single throwaway remark in I Shall Wear Midnight, Esk expresses concern for her son and he is mentioned in The Shepherd's Crown, so perhaps Pratchett intended on expanding on this idea in a later novel. Whether this son is also the son of Simon is unknown but the child of two Wizards might well be remarkable enough for her to be concerned for his safety. In Sourcery it is mentioned that Ipslor's seven sons before Coin are all very powerful wizards, so, presumably, the child of any wizard would also be a powerful wizard. In The Shepherd's Crown, Eskarina opines that he might become an engineer, which may be even more frightening.