The iron represents the life of hard work and drudgery the single mother who narrates the story endures as she raises her children. The mother, as she irons, dwells on her oldest daughter—who she feels didn't get enough of her love and affection growing up. The iron represents everything harsh that kept this poor woman from giving her daughter the kind of life she wishes she could have offered her.
To her daughter, the iron and act of ironing becomes symbolic of her mother. She says to her mother:
Aren't you ever going to finish the ironing, Mother? Whistler painted his mother in a rocker. I'd have to paint mine standing over an ironing board.
If Whistler showed his mother at leisure, sitting in a rocking chair, this mother is shown to always be working. The mother's work never seems to be finished, and the work itself seems to always stand—like the ironing board—between the mother and the child.
At the end of the story, the mother hopes her daughter can have a better future (a better adult life) than she had. She wants her to have more control over her destiny:
make it so there is cause for her to know--that she is more than this dress on the ironing board, helpless before the iron.