According to the story, Morgenbesser was in a New York diner ordering dessert. The waitress told him he had two choices, apple pie and blueberry pie. "Apple," Morgenbesser said.
A few minutes later the waitress came back and hold him, oh yes, they also have cherry pie.
"In that case," said Morgenbesser, "I'll have the blueberry."
Cherry pie is what Arrow calls an "irrelevant alternative." It is irrelevant because, given the chance to order cherry pie, Morgenbesser rejected it. But something you don't want anyways shouldn't cause you to change what you do want.
The Great Flip-Flop is an example of a vote failing to meet independence of irrelevant alternatives.