Barbara Burke is Richard Burke's ex-wife and mother of their two children, Timothy and Michelle. She never appeared on-screen.
In season 2, when Monica Geller meets Barbara's ex-husband Richard for the first time in years, Monica asks how he's been and Richard reveals that he and his wife Barbara got divorced which leads to a relationship between Richard and Monica ("The One Where Ross And Rachel...You Know").
When Monica asks Richard how many girls he slept with, Richards reveals he lost his virginity to Barbara (similarly to how Ross lost his virginity to his own ex-wife, Carol) and that she was his high school sweetheart as their marriage lasted for 30 years ("The One Where Dr. Ramoray Dies").