What is the purpose of Gay's memoir, Hunger: A Memoir of (My) Body?

In her memoir, Hunger: A Memoir of (My) Body, Roxane Gay tells the story of her life as a way of exploring complicated issues like self-image, food, desire, sexual assault, trauma, and our public and private lives. There's not one purpose to this book: it's a multifaceted work. But we can talk a bit about Gay's messages and what she accomplishes in sharing them with a wide audience.
One of the key events in Hunger is the brutal rape that Gay suffers through as a 12-year-old girl. This experience will shape the rest of her life, both in the immediate aftermath and through adulthood. As a young woman, recovering from the assault, we see how rape often causes victims to feel deep shame, fear, and self-loathing. The teenage Gay retreats from the close relationship she previously had with her parents: she doesn't tell them what happened to her, so they can't help her. As time goes on, the shame that she feels erodes her self-confidence:

Hating myself became as natural as breathing. Those boys treated me like nothing so I became nothing.

And she turns to food for comfort and protection. Feeling that it was, at least in part, her own fault that she was "chosen" by the boys who raped her, she decides that being less attractive will prevent history repeating itself.

I ate and ate and ate in the hopes that if I made myself big, my body would be safe. I buried the girl I was because she ran into all kinds of trouble. I tried to erase every memory of her, but she is still there, somewhere... I was trapped in my body, one that I barely recognized or understood, but at least I was safe.

Clearly, one of Gay's objectives is to draw a clear line between rape (or traumatic experiences in general) and the instinct to protect oneself. Not every victim of a crime ends up obese, as Gay did. But in her personal case, she's showing how being fat (that's the author's preferred word to describe herself) is a direct result of the trauma she experienced at the age of 12.
Another purpose of Gay's memoir is to explain what it's like to be fat in a culture that values thinness, physical beauty, and self-control. The world is hostile to fat people, she writes, giving examples from her struggles with dating to the flight attendants who eye her large body as she steps onto a plane. 
Hunger, Gay says, is just a form of desire. One of the objectives of her memoir is to create empathy in the reader: to make her audience consider the ways in which we are all the same. We are all "hungry" in some way, according to Gay. Her book encourages the reader to look around at the world in a different way, assuming that we don't know what kind of trauma any one person has been through, or how it affects his or her current life.