The Cuthberts wanted to adopt a boy, not a girl, but they asked a friend who was going by the orphanage to pick out a good child for them, there was a misunderstanding, so Anne arrives on the train all excited that she was going to have a home. Then she realizes the Cuthberts don't want her, and she is heartbroken. At first the Cuthberts want to return her to the orphanage, but then they decide to keep her after all.
The book tells how the Cuthberts grow to love Anne, and she them.
In reading the book, you learn of Anne's accidents and triumphs, some of them quite funny.
What I really like about this book is the way it all seems so real-life. When you read it you will find yourself cheering Anne on. Trust me, once you start this book you won't want to put it down again until you finish it.
I strongly recommend this book, but it does have some sad parts--Matthew Cuthbert dies near the end of the book. Once you read this, you will want to read the rest of the series, and the rest of L. M. Montgomery's books, too. I would especially recommend reading the three Emily of New Moon books.