Karei Hirosaki is a Manager at Saiun Dormitory, which is Kazuki's dormitory. She's also a widow. She's very kind, calm, warm, and gentle. Basically, all you see her do is sweep outside. And she always wears a mourning dress. But in the show, they don't tell anything much about her.

Spoiler

While never directly stated in the series, there are strong hints that the man that Karei and Shino once loved is related to Kazuki. The first is that Karei pledges to watch over her love from the background, something she still does with Kazuki. Second is that Karei's love was a Shinto priest, while Kazuki is also descended from a line of Shinto priests. And finally is an overlay between Karei's love and Kazuki as Karei reminds Shino of their pledge to watch over their love.

(Source: Wikipedia)