Hag is an insulting name used for a particularly unpleasant or cruel woman.
Harry and Sirius both used this term to refer to Dolores Umbridge during the 1995-1996 school year.
When Umbridge was back at the Ministry under the control of the Death Eaters, serving as the Senior Undersecretary to the Minister and Head of the Muggle-Born Registration Commission, one of the young witches working under her said, "Will the old hag be interrogating Mudbloods all day, does anyone know?" The wizard next to her cautioned her to be quiet (DH13).
José Barboza, the manager of the Brazilian National Team, called the Chasers for the Welsh team "talentless hags." Welsh manager Gwenog Jones promptly threatened to curse his face off:
The Brazil-Wales grudge began in the early days of the tournament when Brazilian manager José Barboza allegedly called the Welsh Chasers ‘talentless hags’ over a few drinks with loose-lipped veteran journalist Rita Skeeter. His insistence that he had been joking did nothing to quell the ire of Welsh manager Gwenog Jones, who threatened to ‘curse the face off' him. In spite of the ICWQC’s ban on ‘managerial trash talk’ - a ban that many believe to have been created with Gwenog in mind - Jones has missed no opportunity to belittle and insult the Brazilians ever since learning that her team would face them in the quarter-finals (Pm: Quidditch World Cup).
A person called a hag is being compared to the ugly, child-eating creature of the same name.