What is the “stream of consciousness” technique in literature, and how is it used in "I Stand Here Ironing"? What is the advantage of this...

The stream of consciousness technique takes a reader inside a character's mind, revealing perceptions, thoughts, and feelings of a character on a conscious or unconscious level.  This technique suggests the flow of thought as well as its content, so at times it may be fragmented or have little logical connection. But, it provides the advantage of letting thought overlap time.  In Tillie Olsen's "I Stand Here Ironing" there is clearly a flow of thought from the monologue of the mother as she talks with the school official and her unconscious attempts to "iron-out" the past regarding her relationship with her daughter.

As she irons, the mother passes back and forth from present to past in her self-doubt and reflections upon the relationship between her daughter and herself: 

I stand her ironing, and what you asked me moves tormented back and forth with the iron.

Initially, the mother expresses her powerlessness over some of what has happened in her daughter's life:

There is all that life that has happened outside of me.

Her monologue conveys the guilt and remorse that the mother feels for being unable to care for her daughter and also work after the father, who "could no longer endure sharing want with us," left her.  With the flow of thought of stream of consciousness, the mother reveals a pattern of poverty and abandonment.  She recalls the old man living near her once saying that she should smile more at Emily; a thought which generates her memory of Emily's sense of humor.  Moving the iron forward, though, the mother reasons that perhaps Emily was happier when she got "a new daddy." 

Other feelings rush into the mother's memory and slide back and forth: times she and her husband left her alone; times she left Emily to give birth to her sister; times Emily was sick and was isolated again at a convalescent home.  But, although

she was too vulnerable for that terrible world of youthful competition, or preening and parading of constant measuring of yourself against every other of envy,

Emily emerges as a talent. "Now suddenly she was Somebody," the mother says, and "as imprisoned in her difference as she had been in anonymity."  The stream of thoughts move back and forth with the iron:  "she tells me everything and nothing."

Finally, as the iron comes to rest, the mother concludes that Emily will find her way, but even in her dredging of the past, the mother

will never total it all....She kept too much in herself....My wisdom came too late.

Resolved, the mother asks the school official to "Let her be," saying that Emily has enough time to live if the school

will help her to know--help make it so there is cause for her to know--that she is more thanthis dress on the ironing board, helpless before the iron.

Through stream of consciousness, passing back and forth from past to an intruding present, the mother structures her own selfhood as well as assessing the pattern between her needs and hurts, guilt and responsiblity, against the hurts and needs of her daughter--the pattern of motherhood.