An offer in which the repercussions for refusing would be so great that to do so would be either be dangerous or ill-advised. It often implies the "offer" is a threat, but this is not always the case. The phrase was coined by Mario Puzo in his 1969 novel The Godfather, and popularized by the 1972 Francis Ford Coppola film adaptation of the same name. If he's not willing to agree to the contract, I might have to bring a few men over and make him an offer he can't refuse. The buyout deal was worth $9 billion to the company, so, really, it was an offer we couldn't refuse.