Ironing was no easy task at the time that this story is set. In fact, ironing has been one of the most enslaving, demanding, and dangerous jobs throughout the history of home economics. All you need to do is do a search on "the history of ironing" online and you will see how the tool itself has been modified hundreds of time for that same reason.
Moreover, the main character is "standing there ironing" setting the record straight and explaining a situation the same way that she is setting the clothes she is ironing straight. It is basically a symbol of being at the bottom of the totem pole: You are there ironing, slaving over something, sacrificing yourself.
That is the basic premise of it all.