Mrs. O'Leary is a woman who lives adjacently to the Turner's House.
Her name is a reference to Catherine O'Leary, who became famous when it was alleged that an accident involving her cow had started the Great Chicago Fire of 1871. She has never actually appeared on the show in person, but her backyard and collection of bees were of slight importance when Timmy Turner, shrunk to the size of a doll, was found and dipped in honey by his friends before being catapulted into this yard with destructive intent. Timmy was saved by a Crimson Chin doll he had earlier wished to life.
In the episode "Boy Toy", Timmy Turner wishes his Crimson Chin doll to life and himself to a doll so that he could share one last adventure with his favorite old toy before he allows his friends to destroy it. Eventually, the Crimson Chin doll takes off without Timmy, and with his doll-form fairy godparents taken by Tootie, doll Timmy is left at the mercy of his friends Chester and A.J., who elect to catapult the likeness of their best friend into the beehives in Mrs. O'Leary's yard, but not before dipping him in honey. Timmy's friends launch him from his treehouse into the adjacent yard, but he is rescued by the Crimson Chin doll and knocked into Vicky's backyard.
After this, Mrs. O'Leary's yard or her beekeeping is never referenced again, and Timmy's usual neighbors are the Dinklebergs.