What's Up With the Title?
Deific Daddy
"The Godfather" isn't just a person who agrees to act as a substitute father in the event of a child's parents' death, as stated during a Christian baptism—though it is that too. It's a term for a mafia Don (invented by Mario Puzo) and a symbol.
The Godfather is a total authority: The mafia doesn't operate as a democracy, but a monarchy, with all the intrigues and rebellions that this involves. So The Godfather is about one man, Vito, trying to retain that position in order for one of his sons to succeed him. It's almost a Shakespearean historical play, like Henry IV (except without Falstaff's comic relief).
You can take the title to refer to either Michael or Vito: Michael ascends to the throne, while Vito gradually lets it go. The meaning of the title, and what it represents, changes too. Vito is more of an old-school Don, unwilling to deal drugs. Michael recognizes that he needs to use unbridled ruthlessness to get ahead and stave off his enemies. At the same time, the Godfather isn't just a criminal: He's someone who tries to preserve an Old World idea of order within the New World. The movie chronicles the history of that attempt.