Affiliation: Order of the Phoenix
Though we've learned bits about James Potter throughout the series, it isn't until Book 7 that we really get to know Harry's mom, Lily (Evans) Potter. Like Hermione, Lily was a very talented Muggle-born witch. It was young Severus Snape, who lived near the Evans family, who first identified Lily as a witch. Through Snape's memories, we watch Lily grow up in Hogwarts. From her friendship with Snape, we see that Lily is compassionate and willing to look beyond appearances – she sees the good in Snape, rather than judging him for being a poor, insecure, and uncared-for child. A brave Gryffindor, she stands up to bullies (including James Potter and Sirius Black) to defend her friend. She also has good judgment and, unlike her childhood best friend, she isn't at all seduced by Dark Magic. What we're left wondering about, however, is what happened to her after she and Snape split ways.
Since the release of Deathly Hallows, many fans have been touched by Lily and Snape's tragic friendship (for example, you'll find tons of fanfiction about what might have happened if she chose Snape over James Potter). During a web chat, one fan asked Rowling if Lily returned Snape's affection. Here's what our author said:
Yes. She might even have grown to love him romantically (she certainly loved him as a friend) if he had not loved Dark Magic so much, and been drawn to such loathesome [sic] people and acts. (source)
At any rate, Lily is remembered fondly by nearly ever character in the Harry Potter series (unlike James, we might add) – her memory serves as a guiding light for Snape, everyone in the Order adored her, her former professors at Hogwarts were impressed by her, and Harry desperately wishes he could have known her. She acts as a model for the kind of loving, self-sacrificing behavior that Rowling promotes and that Harry practices in order to save the wizarding world.