Jack Nicholson is a slow but deadly mafia man, brought up by the Prizzi family. He falls in love with Kathleen Turner, who's a specialist killer hired by the family, but he marries her anyway because he's in love with her. Anjelica Huston is a former lover who's been dishonoured because she cheated on him in a jealous fit.
It's a movie about family honour and its crazy mafioso implications. One mistake by Kathleen leads to very unfortunate consequences for his marriage by which Anjelica manages to get him back.