In our Parsha Tetzaveh, the laws regarding the anointment, the vestments and the Avodah (service) of the Kohanim are enunciated for the Jewish people.
R’ Shimshon Rafael Hirsch, z’l offers this commentary on the Kehunah and the Bigdei Kehunah (the vestments of the Kohanim) in the new Hirsch Chumash (published by Feldheim in 2005 and translated to English by Daniel Haberman), pages 662-663 in Sefer Sh’mot:
The priestly garments must be supplied and owned by the nation. From this fact alone we draw the important conclusion that only when a Kohen dressed in these garments can be considered a Kohen. Only… [in this attire] does he appear as the nation’s servant in the Sanctuary of the Torah. Only thus does his service become the nation’s service in the Sanctuary… Only thus does… his service attain the character of a Mitzvah given to the nation by Hashem in His Torah….