Toosaka, Aoi

Aoi is the childhood friend of Kariya Matou, and became the wife of Tokiomi Toosaka, adopting his surname. She is the mother of Tokiomi's two daughters, Rin and Sakura.

Aoi is a passive and loyal woman who does not interfere with her husband's affairs, described by Kirei Kotomine as the ideal version of a traditional wife. She accepted Tokiomi's proposal with full knowledge of what it meant to marry a mage. While Kariya loved her as well, he peacefully gave up pursuing her affections because she seemed happy accepting Tokiomi's proposal. It is implied that Aoi and Kariya remained in touch, given that her daughters, especially Sakura, were fond of Kariya's company.

(Source: Wikipedia)

Note: "Aoi Toosaka" is the correct spelling of this name per Hepburn romanization, which is used as a MyAnimeList standard.