I
"Aharon died in the 40th year on the first day of the fifth month" (Bamidbar 33:38). Aharon's yahrzeit, Rosh Chodesh Av, is the only date of death in the entire Torah.
The Oznaim LaTorah asks why the date is found here rather than in the earlier, lengthier description of Aharon's death (20:22-29). His answer is based on the premise that the death of tzaddikim atones. (Rashi 20:11). As punishment for the sins of spies, 15,000 people died each year on Tisha B'Av, for a 40 year total of 600,000. However, the last 15,000 were spared, an event celebrated on Tu B'Av (Rashbam Bava Basra 121a).
The Oznaim LaTorah suggests that it was the recent atonement of Aharon's death which spared the 15,000 people. This could not have been known when Aharon died. Therefore, the date is only recorded later, when its significance was realized.
II
Alternatively, the yahrzeit of Aharon is recorded in the parsha which is read every year just before Rosh Chodesh Av. While a tzaddik's death atones, subsequent yahrzeits are days of judgment and misfortune for future generations. (See Shach Yorea Deah 402:10).
Indeed, when Av enters, we reduce joy, and some laws of mourning begin (Orach Chaim 551:1-16), in commemoration of the destruction of the Bais HaMikdash on Tisha B'av. Aharon's death represents the loss of his example, and the failure of Am Yisrael to emulate it, which led to the churban; his death on Rosh Chodesh Av presaged the reduction in joy years later, beginning on his yahrzeit. Chazal highlight a number of times the need to follow in Aharon's footsteps, and the implications of not doing so:
III
The only other yahrzeit which is found in the Torah requires combining two pesukim. "On the first day of the first month, you shall erect the Mishkan" (Shemos 40:2). On that very day (Vayikra 9:1, see Rashi), Nadav and Avihu, the sons of Aharon, perished (10:3).
In fact, these two Rosh Chodesh yahrzeits, of Aharon and of his sons, are the only days when fasting on Rosh Chodesh is encouraged (Orach Chaim 580:1-2). This is relevant even nowadays for a Chasan on his wedding day (Mishna Berurah 429:10).
Despite being Aharon's sons, Nadav and Avihu did not act as his disciples. They did not consult him, or one another (Sifra 10:1), implying a failure to love and pursue peace even with each other. They had no sons (Bamidbar 3:4). They spurned all offers of marriage because they considered themselves above other people (Tanchuma Acharei Mos 7). This attitude is a failure to love even lowly people and thereby draw them closer to Torah.
Since Nadav and Avihu viewed themselves as above and separate from the people, Hashem's Name was sanctified by them (Vayikra 10:3, See Rashi) as they died and were separated from the people. This is the opposite of Aharon, and Moshe, who did not feel that they were higher than others. Rather, they encountered Hashem without any intention for their own personal gain but as mere conduits to influence others (Meshech Chochma 10:3).
Aharon - and a Kohen who followed him - turned away many from sin, and closer to Torah, because he was like an angel (Malachi 2:6-7). An angel stands in one place (see Zecharia 3:6-7), willing to sacrifice his own spiritual advancement for the sake of his students. Only from such a rebbe should one seek Torah (Moed Kattan 17A and introduction to the Sefer Hafla'ahon Maseches Kesubos).
As we commemorate the yahrzeit of Aharon, we must become his disciples. The fast, and the month, of Av will be for joy and for gladness, if we love truth and peace (Zecharia 8:19), the legacies of Aharon.