A fictional baby conceived by anal intercourse and birthed through the anus, just as a regular baby is conceived by sexual intercourse and birthed through the vagina.
In reality it is impossible to impregnate anyone or give birth through the anus. Mentioning or discussing the concept of a butt baby is a pursuit into often intentionally juvenile humour.
John: "Shut up, you butt baby!"
Rick: "Hey, us butt babies are contributing members of society! We are all equal, whether born from the hoo-ha or born from the ha-hoo."