A great deal can be learned about the death of Aharon. It was referred to as מיתת נשיקה, or, the "kiss of death." It was a very sweet and calm departure from this world to the place where he was "gathered unto his people", who awaited him in עולם הבא.
What comforted Aharon as he left this world, was the knowledge that everything he lived for would be carried on by his children. He merited seeing his Priestly garments being placed on his son, Elazar.
Aharon was able to leave this world peacefully as he clearly made his mark on the world. The Torah tells us that the people mourned more for Aharon than Moshe, because Aharon was a lover of peace. He always found ways to create harmony between individuals.
At funerals in Israel, the Chevra Kadisha recites the Mishna from Pirkei Avot: מאין באת ולאן אתה הולך, that one must know from where he came and to where he's going. When one understands what is important on this world and what is not, and when one's priorities are straight, he understands how temporary this world is and the permanence of the next world. Such a person will merit the מיתת נשיקה of Aharon.