The Witch of Montalbino is the mother of principal character Peter Regis. Her country, Montalbino, is considered to be far off from High Norland, where the events of this book take place.
The first we hear of her is when it turns out that she has arranged with Wizard Norland to have her son Peter take up residence with him as an apprentice. Peter himself has written to the wizard, specifying a date when he expects to arrive at the wizard's house, but this turns out to be news to Charmain Baker, who finds Peter knocking emphatically on the door in the afternoon of her first day at the house.
Peter speaks of his mother fairly often, and mostly to mention how she is fond of pointing out his flaws as a magic user. This makes sense, since Peter turns out to be very bad at doing magic -- things always go wrong, no matter how correctly he performs the steps of a spell.
When finally the witch does show up in High Norland, she turns out to be very efficient, very practical, and very willing to say things that others might well take offense at. You might even call her 'bossy,' but probably not to her face.
Eventually some secrets about the witch and her family members come out, which both complicate and improve matters in High Norland, but for most of the novel, these secrets are kept nicely quiet.