By far, the most prominent symbol in the book is the house itself. Look again at the chapter "Bums in the Attic." There is a comparison of the small, crooked, drab house she actually lives in to the one she imagines for herself. One theme of the book is the longing for something more - or a desire to live more comfortably. Esperanza's house is symbolic of this desire. It is the constant reminder of what she does not have materially. On the other hand, another theme presented in the book comes from the idea of hope - hope for something better when I grow up, hope to always have something better in the future... in this way, the house is symbolic of stability and protection from the difficulties of childhood. It gives Esperanza a place to feel safe so that she is able to create and hold on to dreams of a better future for herself.
Another symbol in the book is shoes. Shoes, for Esperanza, are a symbol of feminity, adulthood, sexualty. They are a reminder for her as a child of her desire to be attractive but her struggle to also be independent.
Finally, trees are symbolic of independence and strength. Esperanza takes careful notice of trees throughout her neighborhood and personifies them.
As the previous answer discusses, the family house is definitely one of the most prominent symbols in The House on Mango Street. I'll add a couple more symbols from the book to this discussion: the monkey garden and poems.
First, the poems throughout the book include the children's jump-roping chants, and the poems that Esperanza and other characters write. In the chapter, "Minerva Writes Poems," Esperanza and Minerva read poems they write out loud to each other. Minerva's husband is abusive, and she writes poems at night after her children go to bed. Both Minerva and Esperanza are aspiring poets, and they use language and self-expression as a way to escape. Specifically in this chapter, but also throughout the book, poems symbolize a way for women to express themselves freely and add beauty and creativity to their difficult and limited lives. Poems symbolize a way for women to take back some of their power and create something that is entirely their own.
Second, the monkey garden symbolizes the loss of innocence, the end of childhood, and the ways in which even places of safety and escape can change over time. The monkey garden is similar to the Bible's Garden of Eden--it starts out as a wonderful and safe place for the children to play, but as the book continues and Esperanza grows up, the garden fills with weeds and junk cars and loses its initial magic.