Emily is the ex-girlfriend/friend of Maggie Sawyer. Maggie was Emily's enemy; after cheating on her.
Emily had a five-year relationship with Maggie Sawyer, but Maggie betrayed her, and when Emily knew about it she broke up with her, telling her that she didn't deserve to be happy. These words made a great impression on Maggie.
Years later Emily accidentally stumbled into Maggie and her new girlfriend Alex Danvers, and Alex convinced Maggie to ask Emily to go to dinner with them. Emily initially agreed, but eventually decided not to show up. When Alex went to ask her explanations, she told her that Maggie had betrayed her.