The experience of reading Anne Frank's diary is quite a bit different than reading about the same events in a history textbook. Reading about war, battles, and, in this case, the Holocaust is informational reading which is concentrated on the facts of what happened. Anne's diary is a record of her experiences in the attic. She shares her thoughts and feelings, as well as her hopes and dreams.
Another reason the experience of reading Anne's diary seems a very personal experience is because readers know that it is authentic and unbiased. Oftentimes, people who wrote historical accounts held a bias. History has often been written by the side of those who won wars or who were in charge, and they used propaganda to ensure that they were portrayed in the way they wished to be portrayed. This is absent from Anne's writings. It is her experience, without propaganda or bias. Obviously, it's told from her point of view, but with the honesty of a person who doesn't have a political agenda. Consider how she describes the laws that Jews were subjected to under Hitler's rule:
Our lives were not without anxiety, since our relatives in Germany were suffering under Hitler's anti-Jewish laws. After the pogroms in 1938 my two uncles (my mother's brothers) fled Germany, finding safe refuge in North America. My elderly grandmother came to live with us. She was seventy-three years old at the time. After May 1940 the good times were few and far between: first there was the war, then the capitulation and then the arrival of the Germans, which is when the trouble started for the Jews. Our freedom was severely restricted by a series of anti-Jewish decrees: Jews were required to wear a yellow star: Jews were required to turn in bicycles! Jews were forbidden to use street-cars! Jews were forbidden to ride in cars, even their own! Jews were required to do their shopping between 3 and 5 P.M.! Jews were required to frequent only Jewish-owned barbershops and beauty parlors! Jews were forbidden to be out on the streets between 8 P.M. and 6 A.M.! Jews were forbidden to attend theaters, movies, or any other forms of entertainment; Jews were forbidden to use swimming pools, tennis courts, hockey fields, or any other athletic fields; Jews were forbidden to go rowing; Jews were forbidden to take part in any athletic activity in public; Jews were forbidden to sit in their gardens or those of their friends after 8 P.M.; Jews were forbidden to visit Christians in their homes; Jews were required to attend Jewish schools, etc. You couldn't do this and you couldn't do that, but life went on.
In this passage, Anne reveals the experience of the Jews under Hitler's regime. Hitler put out many forms of propaganda that told a much different story than Anne tells. The experience of reading Anne Frank's diary is also much different than reading Elie Wiesel's Night. Wiesel was also a Jew under Hitler's rule. He was taken to the concentration camps and gives very little detail in his memoir about how the atrocities against the Jews came to pass. Through Anne's eyes, we see these atrocities began with a series of laws that progressively became more oppressive.
Anne's diary is also made more poignant knowing that it was published posthumously, or after her death. Miep Gies, one of the secretaries who worked in the building where Anne and her family hid, found her diary and gave it to Anne's father, the only one of the family to have survived.
Anne doesn't omit anything of the human experience of the horrors of hiding out at the risk of being killed. She describes the fear, the boredom, the squabbles between the eight people living in the annex, and her hopes and desires. It is this human element that makes it personal and universally relatable.