In the old days, when Hickey was loved and adored by all, he used to tell stories of how he caught his dear wife Evelyn having an affair with the Iceman (things like ice and milk used to get delivered back in the day). Hickey told this story as a joke and everyone found it to be a great “gag.” The Iceman proves to be much more than a joke in the end. He comes to symbolize death in the play, which makes him a pretty important figure even he’s never seen.
The title itself, according to O’Neill scholars like Travis Bogard, is "drawn from the story of the wise and foolish virgins in Matthew 25:6," and points to "the description of the coming of the Savior: 'But at midnight there was a cry made, Behold the bridegroom cometh'" (source).
This particular biblical reference fits really well with The Iceman Cometh, because it’s a play about a group of people who are waiting for a savior, but the guy who shows up is definitely not that. Twisting expectation is something O’Neill does throughout the play. Hickey doesn’t turn out to be who the group hoped he would be, Hickey’s plans to help the regulars at Hope’s don’t turn out the way he planned, and a lot of what we’re led to believe about these people’s pasts turns out to be lies.