An autobiography is a prose narrative about some-one's own life.
When a person writes a book about his own life and experiences, the book is an autobiography. When a writer authors a book about someone else's life and experiences, the book is a biography.
The prefix "auto" in autobiography, refers to "self". Loosely, "bio" refers to "person" and "graphy" refers to "writing" or "text".
When we add "auto" to a term that already stands for "person-writing" or text about a person, we then have a phrase that reads "self-person-writing" or text written about the self.
A more tricky distinction comes in determining when a work is a memoir or an autobiography, however, determining whether a book is a biography or an autobiography comes down to authorship.