What is the significance of Sandra Cisneros's quote "I like to think that somehow my family, my Mexicanness, my poverty, all had to do with shaping me into a writer. I like to think my parents were preparing me all along for my life as an artist even though they didn’t know it"?

This short essay by Cisneros is about the ways in which she overcame obstacles, especially in regards to her race, childhood economic status, and shyness, and gained confidence in her abilities. After this quote, Cisneros goes on to describe the ways that her parents, her brothers, and other events in her life shaped who she became as an adult and as an artist. 
Thus, this quote is perhaps the "heart" of the essay. It speaks to one of the essay's main ideas, which is that anything in life—be it good, bad, or confusing—is important in forming our identities. Even though it might seem like some experiences are difficult or inconvenient when they first occur, we often discover the richness and value of these moments later on.
Like the essay's title, we can take the "straw" from our lives and turn it into gold. Cisneros talks about how we can find value in virtually anything from our lives, discussing how certain difficult periods in her life influenced The House on Mango Street. She writes, "How was I to know that I would be documenting and recording the women who sat their sadness on an elbow and stared out the window? It would be the city streets of Chicago that I would later record, as seen through a child's eyes. I've done all kinds of things I didn't think I could do since then." 
The quote speaks to the essay's ideas of the ways in which life is surprising and constantly changing, and to the ways we can practice noticing the rich lessons available all around us, in any situation.