Many psychologists are convinced that birth order has much to do with the development of children's personality.  Researching this topic will reveal books and many studies on birth order.  Using this research, correlate the definition of the first-born's idiosyncrasies with Emily.  Is she the typical first-born child?  With specific reference from the story, define Emily as a typical first-born according to the reports you have located.

Without knowing how your instructor has set up the assignment of the definition essay, I would say you need to look for an abstract concept and then use the story to develop your support.  The story itself shows us a mother reflecting on how limited her life has been because of the demands of being a mother as well as the decisions she's made.  She fears that her daughter may make the same mistakes, seeing some of the same qualities of her youth mirrored in her daughter's behavior.  Her hope is that the daughter can escape the domestic and economic restrictions that have formed her own adult life. 

One suggestion I would make as a topic for a definition essay over this story would be the concept of "mother" or "motherhood" as described in Olsen's story.  Since this story is virtually autobiographical, Olsen is presenting the reader with a portrait of motherhood.  What is she saying about motherhood?  What is the central idea she develops about motherhood?  Once you locate that central idea, find three aspects of motherhood that are described in the story which support your central idea.  These aspects will make up your three body paragraphs, one per paragraph.  Use material from the story to illustrate/support each aspect.   Hope this helps!