Named after Sir Astley Paston Cooper (1768-1841), a famous surgeon and anatomist in Guy's Hospital, London, these are part of the connective tissue found in human breasts that help the breasts keep their roundish shape.
Also known as the ligaments of Cooper, more precisely as the suspensory ligaments of the breast as well as the suspensory ligaments (of Cooper) and other derivatives of the same.
Fans of the book "The House of God" by Samuel Shem will know these as "Cooper's droopers".