Dead Man Walking is a memoir. It's a piece of literary nonfiction that functions as a collection of memories. It's sort of like Walden, only instead of a big old pond, you've got a big old electric chair.
So the book is about personal memories, but Prejean doesn't always keep it personal. Sometimes, she tells you exactly what she's thinking in the way you'd think a first-person memoir would. For example, she says at one point: "It makes me think of my own daddy. It has to be one of life's most special feelings to know that your father is proud of you" (9.13). Basically, she's reminiscing about her dad; you don't get much more personal than that.
Other parts of the book, though, are more essayistic: they're reports. For example, Prejean sometimes includes quotations from the philosopher Albert Camus. Sometimes, she includes statistics—and even, occasionally, bullet points (10.46-48).
Dead Man Walking is a polemic as well as memoir—it's trying to convince you of a political point. But you could also see the polemic as being part of the memoir. Memoirs tell you what the author is like, or who she is—and a big part of who Prejean is is this person who wants you to stop supporting the death penalty.
Basically, Prejean wants to make her story personal so you can see the human side of the issue, but she also doesn't want to seem all wishy-washy or touchy-feely about it, so she also provides a lot of facts and statistics to ground the memoir.