When a girl is on her period, she needs someone, preferably but not neccessarily a tall boy, to snuggle and/or nuzzle with. This person is not a relationship partner, although partners are permitted. They do not give verbal emotional support, they only snuggle. The name originates from the act of snuggling (one snuggles with a cat) and the cause of the snuggling being the menstrual cycle (hence, uterus).
Ugh, my period cramps hurt so much! I need my uterus cat to give me a hug.