Usually used to refer to the head of an
Sicilian crime family/organization (Mafia). Being someone's Godfather was a great honor in Sicilian culture, and he was expected to help in the upbringing of the
baptized child, almost like a
third parent.
The head of a criminal organization would look over all it's members in the same way, while he might not be related to any of them.
The term Godfather didn't really catch on until the movie(s) were released.