Sarah is the mother of Laura Palmer and the wife of Leland Palmer. Laura is found murdered in the pilot episode of Twin Peaks. Sarah's husband Leland has been a bit unstable since the murder, and Sarah doesn't know what's going on.
Sarah has some paranormal powers, and she is known for (on some occasions) predicting the future or seeing people (Bob) no one else sees.
In the Pilot episode, she has a vision of the other half of Laura's necklace (buried by James Hurley) being dug up.