Yui is an artificial intelligence designed to monitor the emotions and mental health of the players in Sword Art Online. Kirito saved her from being deleted by Cardinal by converting and storing her data into his own NerveGear. She later appears in Alfheim Online as a Private Navigation Pixie and helped Kirito locate Asuna. Yui refers to Kirito and Asuna her “Papa” and “Mama” respectively, as they consider Yui their first “daughter” as well.
Source: Frosty McBlizzard on Google+