"You shall sanctify him, for he offers up the food offering of your G‑d; he shall be holy to you"—Leviticus 21:8.
We are commanded to honor and exalt the seed of Aaron, the kohanim (priests), and to acknowledge their holiness.
This mitzvah applies whether or not the specific priest desires such honor. This mitzvah applies also to maimed kohanim, though they are not eligible to serve in the Holy Temple.
We fulfill this mitzvah by honoring the priest with the first aliyah to the Torah and leading the Grace after Meals, and by allowing him to take the first choice portion of food.
Honoring the kohanim is, in effect, honoring G‑d, who chose them to serve Him [in the Holy Temple] and offer the sacrifices.