Binky is the infant son of Walter and Madge Nelson, and the brother of Walter Jr. and Tina Nelson.  He is being brought up in the Nelson family tradition of criminal behavior, and seems to be developing a knack for it, occasionally demonstrating quite a talent for devious behavior in spite of his general innocence.  Like the rest of the Nelson family, Binky's criminal exploits have already landed him a short stint in jail and a criminal record, meaning he's been photographed and fingerprinted as well.

Binky's entire comfort revolves around his pacifier, which has a skull-shaped fob dangling from it.  He becomes utterly inconsolable whenever the pacifier is lost or misplaced, and will do anything he has to in order to regain it