1. Traditionally, a Southern USA expression for a grandfather, probably from "Papa's Daddy."
2. By extension, a traditionally masculine (non-Metrosexual) man who plays a "Daddy" role emotionally, sexually or financially.
-- "Who's that man I saw you with at the cafeteria? He's old enough to be your father."
-- "Dear heart, he's almost old enough to be my grandfather and I am just lovin' it! Papadaddy! Papadaddy!"