1920s slang for a small town salesmen who makes a show of spending his money on trips to the big cities. Some places imply that it carried a connotation of a person spending above his ability, but the Louis Armstrong song and the play the George Kaufman play seem to suggest that they are wealthy enough to afford kept women and finance Broadway shows. The common theme is that they have money but lack sophistication.
Finding the exact origin of the word was difficult, but I ultimately found a New Yorker article from 31 October, 1925, that pinpoints it. Mary “Texas” Guinan was a saloon keeper and famous personality in New York during prohibition used the term to refer to Samuel Balcom. Balcom supplied her restaurants, and others, with dairy products, and spent freely in the establishments. “He’s our Butter-and-Egg Man,” she would say of him.
In my searches, I came across this quote attributed to Ogden Nash. I think I’ll end with it: “Because in America a rich butter-and-egg man is only a rich butter-and-egg man or at most an honorary LL.D of some hungry university, but in England why before he knows it he is Sir Benjamin Buttery, Bart.”