Da Vinci is the third Servant that was summoned to Chaldea successfully. She's a Special Honorary Advisor of Chaldea's Tech Division. Her class is Caster.
She was called “the universal genius” that left achievements in many fields in Europe. She loves her own masterpiece “Mona Lisa” so much that she imitates Mona Lisa’s appearance while existing in this world. During the ray-shift, da Vinci supports the team as (with?) technical backup.

(Source: anime.fate-go.us)