Why does Hashem refer to the Bigdei Kehunah as "Bigdei Kodesh"?
Rashi (in Pasuk 4): Because they made them from the donaions that he owners sanctified in the Name of Hashem. 1
See Sifsei Chachamim.
In whose 'honor' did Aharon wear the Bigdei Kehunah?
Ramban #1: Aharon himself was honored and glorified wearing such honorable and glorious Begadim 1 - seeing as these garments are robes that were worn by royalty in those days. 2
Ramban #2 (according to Kabalah): They should manufacture Begadim for Aharon to wear in honor of the G-d who dwells in their midst and who is the glory of their strength. 3 Also, it is to glorify the Beis ha'Mikdash, the location of Hashem's Feet and which is honored with the Kavod of Hashem. 4
Seforno: In honor of Hashem, in whose service he wore them.
As the Pasuk indicates in Yeshayah, 61:10. See also Shmuel 2. 13:18 (Ramban).
See Ramban, who cites proofs of this with regard to most of the Kohen Gadol's Begadim with many Pesukim from Tanach in support. He also explains that this is why Ya'akov made Yosef a Kesones Tashbeitz (equivalent to the tunic that the Kohanim wore - as the Ramban explained in Terumah, Sh'mos 25:18).
See Tehilim, 89:18. In effect, Hashem is glorified by Yisrael and the Beis ha'Mikdash (See Yeshayah, 44:23, 60:7 [Ramban]).
And the Torah use the same expression later, in Pasuk 40, in connection with the Begadim of the Kohanim Hedyotim.
What are the connotations of "Tif'eres"?
Seforno: Aharon struck awe upon whoever was in his vicinity, all of whom were his Talmidim, 1 whose names he wore on his heart and on his shoulders. 2
Targum Onkelos and Targum Yonasan: It has connotations of praise.
Oznayim la'Torah (citing the Rambam in Hilchos K'lei Mikdash, 8:4): "le'Chavod u'le'Sif'eres" also has connotations regarding the way the Kohen wears them - that they should be clean, neat and the right size. Consequently, if they are dirty, torn, too long or too short, his Avodah is Pasul.
Peirush: With reference to all of Yisrael - as the Torah writes in Vezos ha'Berachah, Devarim, 33:10.
On the stones of the Choshen and the Eifod, respectively.
If the Begadim of the Kohen Gadol were designated for Aharon and his descendents, what did Moshe wear when he served in the capacity of Kohen Gadol during the seven days of inauguration?
Rashi (34a): Moshe was a Zar regarding Bigdei Kehunah, and could not wear them - as the Torah writes here "Ve'asisa Bigdei Kodesh le'Aharon Achicha" (to preclude Moshe). He served as Kohen Gadol by Divine command, and the Torah did not mention what he wore. Tosfos (34a) - one opinion (in Zevachim 101b) holds that he served as Kohen Gadol all forty years! The Gemara asked about the Milu'im, for the Bigdei Kehunah were not yet sanctified. The Ri of Orleans explains that, during the Milu'im, the Mishkan was like a Bamah, and Bigdei Kehunah were therefore not required.
Much like the Kittel that we wear at the Seider and on Yom Kipur.
