In order to quell the complaints about Aaron the High Priest being undeserving for the High Priesthood, HaShem commanded Moses to tell each of the princes of the twelve tribes to inscribe their name on a staff and leave it in the Tent of Meeting, along with Aaron's stick. The next morning, Aaron's stick sprouted flowers and almonds. It was thus clear that HaShem had selected Aaron to be His emissary to the Nation of Israel in the capacity of Kohen Gadol. However, the reason as to why Aaron required a new appointment to his already-previously held position of Kohen Gadol requires explication. Rabbi Meir Don Plotzky of Ostrova explains that when Korah gathered supporters to dispute Aaron's claim to the Kehuna Gedolah, Rashi says that he gathered two-hundred and fifty judges from the Sanhedrin court. Accordingly, Rabbi Plotsky says, since the Kohen Gadol is verbally appointed and removed from his position by the Sanhedrin, when Korah's "court" ruled that Aaron was unfit for service, Aaron actually lost his halachik status as the Kohen Gadol. Therefore, it was required that Aaron should specifically be chosen again as the Kohen Gadol by means of his staff which budded almonds and flowers.
Nonetheless, this explanation is only true according to the understanding of Maimonides who ruled according to the Tosefta that the Sanhedrin has the right to appoint and impeach the Kohen Gadol; however, Tosafos understand that the king and fellow Kohanim possess that capability. Perhaps one can explain that since Moses was the King of the Jewish People, Aaron could not be appointed Kohen Gadol by the king because the king has a vested interest in his appointment since they were brothers. Therefore, perhaps even Tosafos would agree that when the king is disqualified from making an appointment to the Kehuna Gedolah, then the Sanhedrin holds the power to make such an appointment.
 Numbers 17:16-26
 See Yoma 19a which concludes that the Kohen Gadol is agent of G-d, not of the people.
 Kli Chemda to Deuteronomy 1:17
 See Rashi to Parshas Korach, especially to Numbers 16:1
 Laws of the Vessels of the Sanctuary 4:15
 Tractate Sanhedrin, Chapter 3
 To Yoma 12b
 See Zevachim 102b