Let's break down the word biography.
bio means life
graphy is Greek for writing
So, biography mean the writing about someone's life.
auto means self
So, autobiography means the story of someone's life written by the person who lived it.
An autobiography is a book that explains the life of a person, AND the story of the book is the author of the book. For instances, if a book about Steve Jobs was an autobiography, Steve Jobs actually wrote it. A biography is similar to an autobiography, but someone else wrote the book. When someone wrote about Steve Jobs that wasn't Steve Jobs, you would call that a biography.
This is an example picture of an autobiography and a biography (click to enlarge):
The one about Lemony Snicket (my favorite author) is pretty obvious because in the title it reveals that it is an autobiography. Mr. Snicket wrote his life story.