Hagatha and Nagatha are twin sisters who appeared in "Illusion Confusion!" The main way to tell them apart is their headbands—Hagatha wears red, Nagatha wears white—though they also have slightly different eyebrows.
The two run an operation in and around a notoriously haunted forest. Hagatha lives deep in the woods, where she rents out Hoothoot to travelers trying to navigate past the Ghost-types that roam there. The Hoothoot use Foresight to guide people safely past Gastly, Haunter, and Gengar. Nagatha handles the business side, living at the forest's edge and collecting the Hoothoot once trainers make it through.
When Ash and his friends stumbled into the forest, they were immediately chased by illusions—until Gary showed up with his own rented Hoothoot and temporarily helped them out. They eventually found Hagatha, who scared the hell out of Brock and Ash when they first met her. Brock was so thrown off by her appearance that he assumed she had to be an illusion. Hagatha wasn't thrilled about their reaction and screamed at both of them before renting them a Hoothoot that had never actually guided anyone through the forest before—not exactly the most reassuring choice.
After making it out, Ash's group ran into Nagatha, who was quick to brag about being much better looking than her sister, despite them being identical. She made a point of it anyway.
Content compiled by AnimeList.moe from publicly available sources.