How would I write a "significance" essay on this play?
First off, you'll need to decide what you want to write about - do you want to write about characters? Theme? Style?
Certainly the characters have significant impact on each other - Ruth's worries about what others think, Beatrice's losses of her father and husband, Tillie's awkwardness. All of these qualities lead the characters to behave in ways that impact the others.
In terms of theme, you could look at how dreams, for example, impact the characters' decisions and ways of treating each other. Beatrice's dreams are consistently shattered and her daughters often pay the price for her losses. Ruth's dreams cause her to have seizures. Other themes also have a significant impact on the characters - how each one feels about herself (mostly negative) also impacts decision-making.
Lastly, you could focus on style. How did Zindel's writing style impact the effect of the play? You could look at his use of voice over, how hearing Tillie's inner thoughts impacts the story-telling and character development. Another significant aspect of the style is his use of comedic elements, like Janice Vickery's speech. Does this use of comedy aid or hinder the communication of Zindel's theme?
It's a great play - I hope you're liking it!