It is derived from the hypothetical situation in which Frank Sinatra has an affair with his own daughter, Nancy, and they bestow their new inbred love child with the moniker "Nank," a portmanteau of their own names.
This is preferred over "retarded" or "gay" because of its low level of offense to various groups of people (i.e., individuals who actually are mentally challenged or gay). Frank and Nancy might not prefer it, but that's what they get for engaging in fictional incest.
"My anti-Semite grandmother cut me out of her will because my wife's Jewish."
"Man, that's nank."
"I read somewhere that Frank Sinatra had sex with his daughter and the two bore a child together."
"Ew, that's nank."
"That toddler just put toothpaste in his eye."
"Oh, that's Nank."