Why is the exact date of Aharon's petira mentioned? We don't find this by other people. Secondly, why, when saying Aharon’s name this time, does the Torah add “hakohen”?
The Trumas Hadeshen addresses the first question. Right after Aharon's petira, the Torah says, הכנעני וישמע. They heard of our tragedy of losing Aharon and waged war against the Yidden. Why davka at that specific time did they attack? The answer is because they realized then that the month of Av is one in which the mazal of Klal Yisroel is not good. As Chazal teach us, one should postpone a court case scheduled for this month until after Av. They therefore struck klal Yisroel at that time, with the date playing a pivotal role in the sequence of events.
Rabbeinu Bechaye in his sefer Kad Hakemach offers another thought. The Torah wanted to teach us the concept of מיתתן שקולה אלוקינו בית כשריפת צדיקים של. Hence, מאהרן יתת coincided with Rosh Chodesh Av, the month of the churban. The Pardes Yosef adds that this is why the Torah only wrote the date in this parsha and not in Parshas Chukas where Aharon's petira is also cited.
Because chodesh Av commences this week, we will offer one more machshava. Aharon was the exemplar of שלום ורודף אוהב, the quintessential promoter of achdus. It is no small wonder that with his passing in the month of Av, there was a weakening of unity among us, and the aveira of sinas chinam was able to rear its ugly head. Maybe that's why it says Aharon Hakohen. The very reason he became the Kohen Gadol was because of his special middah of having a lev tov and “farginning” yenem. And as the Sfas Emes writes: Aharon's z’chus should stand by us at this time of year, and in his merit, we should be zocheh to the rebuilding of the Beis Hamikdash b’karov!