Her name means "protector", and Frigg gave her the duty to protect men and to console grieving mortals.
In the Völuspá, Hlín also appears to be another name for Frigg herself. In the series of battles that take place during Ragnarök, Odin fights against and is killed by Fenrir:
If Hlín does refer to Frigg then her first sorrow was the death of Baldr.