In addition to the overarching poignant tone to the writing of Anne Frank, the perspicacity of one so young is intriguing. Her diary is a personal account of the fear inspired by the Nazi regime as well as a recording of maturation.
This question certainly needs to be moved to the Discussion section of eNotes. I am sure you will receive many different relevant answers on your question there.
That being said, Frank's diary resonates with so many readers based upon the fact that she offers a moving first-person view of Jewish suffering during the Holocaust. Given that she is both a girl and a survivor, many readers immediately sympathises with her. It is not very often that a girl is able to offer such a compelling first-hand story which is embraced by millions.
Both Elie Wiesel (Night) and Viktor Frankl (Man's Search For Meaning) offer first-hand accounts of the Holocaust, but have failed to have the same impact on the majority of society based upon Frank's novel being so widely used in education. (I am not saying that Wiesel and Frankl have not written wonderful books, in fact they are both amazing. What is being stated is that they are simply not as widely read and used in schools.)
Part of the reason so many readers are moved by this account is that the context of Anne Frank's writing is so tragic, since it is known that she did not survive her imprisonment in the camp. The irony of her diary is that she hoped for a safe future for her family and they were captured. There is also an irony in Anne's inherent optimism, her belief that people are good at hear deep down.
Her diary is also a very accessible and honest document of an ordinary life that only became extraordinary due to the extreme happenings during World War II. Apart from the dramatic situation she was in, hiding from the Nazis, her life was similar to any teenage girl's; she complained about daily hardships, had hopes and dreams for the future, and was worried for her family.