Rizpah was a concubine of King Saul, and the mother of two of his sons, Armoni and Mephibosheth (not to be confused with Jonathan's son of the same name).
During David's reign, there was a three-year famine. When David inquired of the Lord, he was told it was because of Saul's bloodguilt for slaughtering the Gibeonites.
To make amends, David allowed the Gibeonites to execute seven of Saul's descendants, including Rizpah's two sons.
Rizpah's actions following this event were remarkable. She stayed with the bodies of her sons and the other executed men, protecting them from scavengers day and night for months.
When David heard about Rizpah's devoted vigil, he was moved to properly bury Saul and Jonathan's bones, along with the remains of the seven men who had been executed.
This act of David's helped to bring closure to the bloodguilt and the famine ended.