At the beginning of Parshas Acharei Mos, the Torah states that the Kohen Gadol may not come into the Kodesh Hakodoshim except when doing the avodah on Yom Kippur. "Speak to Aaron your brother - he shall not come at all times into the Kodesh. (16:2)" Since the posuk addresses Aaron Hakohen, it would seem that this halacha applied not only to Kohanim Gedolim throughout the generations, but even to Aaron himself.
However, the Vilna Gaon suggested based on a Midrash that as long as Aaron followed the exact order of the avodah of Yom Kippur, he was permitted to enter the Kodesh Hakodoshim any day of the year. That is what the posuk means when it says, "With this shall Aaron come to the Kodesh, with a bull...and a ram..." (16:3) - namely, that if Aaron performed the same avodah that he did on Yom Kippur, he was always allowed to enter the Kodesh Hakodoshim. But all subsequent Kohanim Gedolim did not share the same privilege. They were allowed to enter the Kodesh Hakodoshim only on Yom Kippur. (see Meshech Chochmah who interprets the Vilna Gaon's comment differently) What was so special about Aaron that he was permitted to enter the Kodesh Hakodoshim any day of the year?
When Hashem first asks Moshe Rabbeinu to become the leader of Klal Yisrael, Moshe hesitates. He begs Hashem, "Please send through whomever you will send. (Shemos 4:13)" Rashi explains that Moshe was concerned that it would be insulting to his older brother Aaron if he became the leader. Hashem responds that Aaron will join Moshe in his mission, and moreover, "Behold he is going out to meet you, and when he sees you he will rejoice in his heart. (Shemos 4:14)" Rashi quotes from the Midrash that Hashem was telling Moshe, "It is not as you think, that Aaron will resent you because you are becoming the leader, but rather he will feel happy for you in his heart." The Midrash concludes that for this heartfelt rejoicing, Aaron merited to become the Kohen Gadol who wears the choshen which is placed over the heart.
Aaron was samei'ach b'chelko - he was satisfied and content with his own portion. He was not jealous of his brother Moshe. To the contrary, he felt happy for him, with his full heart. The Mishna (Avos 2:9) says that Reb Yochanan ben Zakkai asked his talmidim to go figure out what is most important character trait. Each one returned with a different response. Reb Elazar ben Arach suggested that the best middah is leiv tov - a good heart - and the Mishna concludes that Reb Yochanan ben Zakkai agreed with him. Why is a good heart the most important middah? The Rambam (on the mishna there) explains that all character traits are developed in the heart, so a good heart will lead a person to perfection in all of his middos. Rabbeinu Yona elaborates that if one has a good heart "all of his character traits will be proper, his attitudes will be balanced, and as a result, he will be samei'ach b'chelko."
It is the middah of leiv tov that leads a person to be samei'ach b'chelko. Someone who has a good heart is not motivated by self-interest. His sole desire is to promote the agenda of the Ribbono Shel Olam and to increase kvod shamayim in the world. All he wants is that each individual should achieve his full potential and be able to serve Hakadosh Boruch Hu in the best possible way. Such a person will naturally be sameiach b'chelko - he will be happy with his portion in life - because the key for him is not that he achieve a position of prominence, but rather that the will of the Ribbono Shel Olam should be fulfilled.
Aaron Hakohen was that kind of person. He had a leiv tov. He deeply cared about each individual. That is why he was rodeif shalom (Avos 1:12) - he pursued peace - even though initially he was resented and vilified by those who wished to continue arguing (see Maseches Kallah Rabasi 3). Aaron's concern for peace was more important to him than dignity and honor. It is not surprising that Aaron felt content and happy when his brother Moshe became the leader of Klal Yisrael because Aaron was never concerned about himself; his goal was always to advance Hakadosh Boruch Hu's agenda. So it did not matter to him who played a more prominent role. The key was simply that the mission should be accomplished.
It is precisely for this reason that Aaron was chosen to become the Kohen Gadol and to wear the choshen on his heart because the Kohen Gadol represents all of Klal Yisrael in the Beis HaMikdash. Only someone who is humble and self-less and has a heartfelt love for every Jew can serve as Kohen Gadol. Aaron was the paradigm of such a personality. It was Aaron's leiv tov that gave him the merit to wear the choshen on his heart.
Perhaps this is why Aaron was also given the special privilege to enter the Kodesh Hakodoshim any day of the year because Aaron was greater than any other Kohen Gadol in history. His humility, his lowly spirit, and his leiv tov were something extra-special. A person with such middos draws the Shechina closer to him. As the navi Yeshaya proclaims, "So said the exalted and uplifted One...I dwell in exaltedness and holiness, but I am with the dakah u'shfal ruach - the despondent and the lowly of spirit. (Yeshaya 57:15)" The Shechina seeks out those who are humble and unassuming. It attaches itself to individuals who are modest and self-effacing. That is why Aaron, the quintessential sh'fal ruach, was always welcome in the Kodesh Hakodoshim.
Aaron Hakohen was unique. But his attitude is a model for every Jew. The goal of an eved Hashem should never be to promote himself or his personal agenda. It is when we act with humility and a leiv tov that we attract the Shechina and we raise ourselves to a higher level.