Farnese is a noblewoman who led the Holy See's ceremonial guard, the Holy Iron Chain Knights. Since this position has been traditionally held by a woman, Farnese was appointed during her stay at the convent she was sent to by her father, Federico Vandimion.
A bit of a pyromaniac (and possibly a pyrophiliac), Farnese's habit of maniacally burning things she didn't like, along with her lack of empathy due to her poor upbringing provoked her to hunt down and burn supposed witches and pagans at the stake. This fueled a secret sadistic pleasure that she constantly tried to deny.
She and Serpico left their Holy See positions after her faith was shattered during the devastation of Albion and the events surrounding Griffith's reincarnation. She then chose to follow Guts in hopes of learning more about the world and has changed into a more sympathetic human being. Since then, Farnese has begun to study witchcraft under Schierke's tutelage. Farnese also seems to have developed a crush on Guts which becomes evident in chapter 287 and 288 of the manga.
Farnese is primarily Casca's care taker and thus rarely involves herself in battles. She and Casca both received enchanted chainmail shirts made of silver as well as a silver short sword for protection against creatures from the astral plane. During Ganishka's raid on Vritanis, she also received a trio of snake-like homonculi created by Schierke from thorn vines which Farnese remote controls with a vine ring.