"Breaking out" moves back and forth between the thoughts of an empowered female, designated by "I," and a little girl who feels powerless, indicated by an "i." They are both the same person, and the poem shows how the scared and questioning little girl grows powerful in two ways, first, by rejecting the domestic life led by her housewife mother and second, by breaking the yardstick her parents used to beat her.
In the first four stanzas, the little girl questions the life of housework that she, as a female, is being raised to lead. She doesn't see any need for using the "mangle" to iron clothes and she is not interested in the "stuffed sausage bag" of the vacuum cleaner. She can't understand why her mother submits to such drudgery, but knows she will not follow in her mother's footsteps.
In school, when she reads about the Greek Sisyphus, who was sent to Hades and had to roll a rock up a hill, always to have it slip from his grasp and roll to the bottom when he was half way up, so that he had to start over and over, the girl connects this to her mother's life of housework:
it was her I
thought of, housewife scrubbing
on raw knees as the factory rained ash.
In the second part of the poem, the girl describes being beaten and how painful it is. Finally, she breaks the yardstick that is used to beat her, and is surprised at how easy it is to do so. Breaking the yardstick doesn't end the beatings, but it does give her a sense of power.
Piercy sums up the poem's meaning in the final stanza:
This is not a tale of innocence lost but power gained : I would not be Sisyphus, there were things that I should learn to break.
The final stanza means she has gained power by deciding not to become a housewife ("Sisyphus") and by learning she can "break" what oppresses her, like the yardstick used to beat her.