What is the importance of the tree in the backyard?

The tree represents a "home".

In this chapter we meet the new inhabitant of Cathy's house, Meme Ortiz. Esperanza describes Meme's sheepdogs and, as homes are important to her, paints a verbal picture of Meme's family's new, ramshackle home. Esperanza then focuses on the property's one crowning glory: a giant tree which is both home to a family of squirrels and the sight of the First Annual Tarzan Jumping Contest, which Meme won at the cost of two broken arms.