donut bun with the base of it is a half-finished donut bun; the loose hair that comes out of it (around the base of the bun) is being plaited into a half or full Dutch braid; the end of the braid is being wrapped around the bun and finally tucked under and hidden

A bun is a type of hairstyle in which the hair is pulled back from the face, twisted or plaited, and wrapped in a circular coil around itself, typically on top or back of the head or just above the neck. A bun can be secured with a hair tie, barrette, bobby pins, one or more hair sticks, a hairnet, or a pen or pencil. Hair may also be wrapped around a piece called a "rat".^[1][2] Alternatively, hair bun inserts, or sometimes rolled up socks, may also be used to create donut-shaped buns.^[3] Buns may be tightly gathered, or loose and more informal