Also in the film, Al Pacino explains to Diane Keaton that "my father made him an offer he couldn't refuse," regarding a prior incident.
In both cases, the "offer" was the threat of death. Today, the words are commonly associated with business and negotiation tactics. As the words are used today, the "offer" is meant to provide an irresistable winning opportunity, or to suffer unfavorable consequences that are far less dramatic than what is portrayed.
Other famous lines from the movie:
A man who doesn't spend time with his family can never be a real man. ~ Don Corleone to Johnny Fontane
Don't ever tell anyone outside of the family what you are thinking again. ~ Don Corleone to Sonny
Fredo, you're my older brother and I love you. But don't ever take sides against the family again, ever. ~ Michael to Fredo
I spend my life trying not to be careless. Women and children can be careless, but not men. ~ Don Corleone to Michael
It's not personal. It is strictly business. ~ Michael Corleone