Po' boy sandwiches originated in New Orleans during a transit worker strike in the late 1920s. The sandwich's name is a reference to the fact that these transit workers didn't have a lot of money because they weren't working. During the strike, the Martin brothers, who were sandwich-shop owners and former streetcar operators, offered free sandwiches to the strikers.
When these strikers would enter the Martin Brothers restaurant, the workers would note that another "po' boy" was waiting to be fed. The latter half of the word "poor" is naturally dropped when spoken with a Southern accent, making it sound like "po'" instead of a fully enunciated "poor."