Video: Most animals don't menstruate. If they don't use their uterine lining, they simply reabsorb it. Only bats, monkeys, and apes take the drastic and seemingly-wasteful step of pitching out the entire thing. And humans toss it out more often than any other animal.
This Ted-Ed video outlines one hypothesis for why menstruation evolved — it's the aftermath of a strict screening process that selects embryos best able to invade uterine tissues and start manipulating their mother's metabolism. [Ted-Ed [Emera et al. 2012]]