The Diary of Anne Frank is so famous, in my opinion, because it is an intimate look into an historical event and the life of the young girl who lived it. This diary takes the reader into the hiding place with Anne and her family, into their day to day life, and into their emotions and experiences--something that no other historical account has ever been able to do before or since.
The Diary of Anne Frank is as famous as it is for literary and non-literary reasons.
The literary reasons are its honesty and the quality of its descriptions of character and emotion.
To be frank, those qualities are probably less important than its non-literary qualities. It was published soon after World War II, in a time when the entire world was still trying to make sense of the Holocaust. It was therefore the first firsthand account many people read of life during the Nazi regime. In many cases, it is the only one read.
Frank's character is easy to identify with; she seems likable and innocent. To read about such a person staying as positive in the midst of what we know to be horrific makes the account, and her, deeply sympathetic.
The Anne Frank diary is very famous becase it was such an historical event for such the young girl who had to live it the diary had the emotion and pain that such a young girl went through for 25 months scared and hopeless of what was going to happen next. It is also in a way a short synopsis of her life before the Holocaust.