I live in Missouri and my daughters father said he wants to give up rights to her, can he do this and what exactly does this mean to Terminate parental rights?

Most states do not allow a father to terminate his rights unless there is another father to adopt so that the child is support, at least financially, by two parents. Have you browsed through the information in LawInfo's Free Legal Resource Center to learn more about your issue yet? See: http://www.lawinfo.com/consumer.html and http://resources.lawinfo.com/en/index.html. You can certainly try to speak to a lawyer to determine what legal options may be available. In the meantime, you may be able to learn more on your own. Search the "Free Legal Resources" tab, or browse the Consumer Resources. Good luck.