Mordane is Winterfell's septa (priestess) for Westeros's main religion, the Faith of the Seven. She is also in charge of teaching the daughters of Winterfell the ways of being a proper lady.
After Eddard Stark accepts the title of Hand of the King, Septa Mordane travels to King's Landing together with the Starks. She is mostly seen tutoring the girls or discussing recent events with Sansa.
After Joffrey Baratheon comes to power and accuse the Starks of treason, she is captured by Lannister guardsmen, beheaded and has her head displayed on a spike, where Joffrey shows her off to a mortified Sansa.