As investing the priest with official garments was a recognition before men of the official position of the person (see Exodus 28:3 note), so the anointing him with oil was an acknowledgment that all fitness for his office, all the powers with which he would rightly fulfill its duties, must come from the Lord.
So, again, with the sanctification of the holy things. Each of them was intended by divine wisdom to convey a spiritual meaning to the mind of man. They were means of grace to the devout worshipper. The oil poured upon them was a recognition of this fact, and at the same time it made them holy and set them apart from all profane and ordinary uses. On kindred grounds, though to express another idea, the altar was to be sanctified also by blood. See Leviticus 8:15 note.