The most important incidents happen after the diary stops. It ends eerily, and we know what happened next. When Anne stops writing, we know it means that their two year struggle to evade the Nazis has ended, and we can only wonder what happened. How were they caught? Who survived? Where did they go? Only the history books tell us this.
You will get many answers to this question. I think one important incident from the Diary will be the most evident one in that the family has been forced into hiding from the Nazis in the Secret Annexe. The diary's structure and content is entirely contingent on how life in the Secret Annexe develops. I would actually say that the second important incident in the diary is the relationship that Anne has with her parents. This is important because it helps to shape the arc of Anne's development as a human being. The first incident is important from a political point of view because it highlights the terror of the Nazis and the hold they had on much of continental Europe at the height of their power. I think that the second incident is important from a personal point of view because it helps to make Anne's narrative a universal one of adolescence. In the midst of unspeakable horror and tragedy, Anne's relationship with her parents shows how human she really is and how while the Nazis sought to destroy everything, they could not really eliminate the universality of the human experience and what connects us as individuals, as evidenced in Anne's diary.