You shall make holy clothes for your brother Aaron, for glory and splendor (Exodus 28:2)
The kohanim (priests) had special uniforms that they were to wear while performing the service. A regular kohein had four such garments, while the Kohein Gadol (High Priest) had eight. All of chapter 28, which is half of parshas Tetzaveh, describes the various bigdei kehunah, priestly vestments.
The four garments of a regular kohein were: the kesones, a long tunic; michnasayim, short pants worn underneath; migba’as, a hat; and avneit, a belt. The additional garments of the Kohein include: the me’il, a robe; the choshen, a breastplate; the ephod, kind of an apron that held the choshen; and the tzitz, a metal plate inscribed with the words “Holy to God,” which was worn on the forehead. The Kohein Gadol also wore a different kind of hat than the regular kohanim. Instead of a migba’as, the Kohein Gadol wore a mitznefes, which was a turban.
The Torah says up front why kohanim wear special clothes when they serve in the Temple or Tabernacle: for glory and splendor. How awe-inspiring would it be if the kohanim tromped around in the Temple wearing jeans and work boots? Of if they wore their pajamas to work? Most occupations have a uniform of some type, whether it’s a suit and tie or a diving helmet. The bigdei kehuna were specially designed to instill the proper awe in those who wore them and in those who visited the Temple.
The Torah says (Exodus 29:9) that the kohanim should be dressed and their priesthood would be upon them. Conversely, at a time when a kohein was out of uniform, he could not perform the service. If a kohein officiated and he wasn’t properly dressed, the service was invalid. (See Talmud Zevachim 17b.)
The obligation for the kohanim to wear special clothes only applies to male kohanim in Temple times. It is discussed by the Talmud throughout the second chapter of the tractate of Zevachim and elsewhere. It is codified in the Mishneh Torah in the tenth chapter of Hilchos Klei HaMikdash and is #33 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.