Before 午 marked noon, its earliest forms pictured a wooden pestle used to pound grain: a long shaft with thicker ends. That old object sense later moved into 杵, while 午 was borrowed for another word with a similar sound and became the seventh Earthly Branch. Because that branch named the period around midday, 午 grew into the everyday time-word you see in 中午, “noon”.
A piece of culture
A two-hour place on the old clock Traditional Chinese timekeeping divided the day into twelve two-hour periods. 午时 / 午時 ran roughly from 11 a.m. to 1 p.m., with the sun highest near its middle. Modern Chinese still carries that older clock in 中午, “noon”, 午饭 / 午飯, “lunch”, and 下午, “afternoon”. One small character turns the middle of the day into a family of useful time words.