Then shalt thou take the anointing oil - It appears, from Isaiah 61:1, that anointing with oil, in consecrating a person to any important office, whether civil or religious, was considered as an emblem of the communication of the gifts and graces of the Holy Spirit. This ceremony was used on three occasions, viz., the installation of prophets, priests, and kings, into their respective offices. But why should such an anointing be deemed necessary? Because the common sense of men taught them that all good, whether spiritual or secular, must come from God, its origin and cause. Hence it was taken for granted,
1. That no man could foretell events unless inspired by the Spirit of God. And therefore the prophet was anointed, to signify the communication of the Spirit of wisdom and knowledge.
2. That no person could offer an acceptable sacrifice to God for the sins of men, or profitably minister in holy things, unless enlightened, influenced, and directed by the Spirit of grace and holiness. Hence the priest was anointed, to signify his being Divinely qualified for the due performance of his sacred functions.
3. That no man could enact just and equitable laws, which should have the prosperity of the community and the welfare of the individual continually in view, or could use the power confided to him only for the suppression of vice and the encouragement of virtue, but that man who was ever under the inspiration of the Almighty.
Hence kings were inaugurated by anointing with oil. Two of these officers only exist in all civilized nations, the sacerdotal and regal; and in some countries the priest and king are still consecrated by anointing. In the Hebrew language משח mashach signifies to anoint, and משיח mashiach, the anointed person. But as no man was ever dignified by holding the three offices, so no person ever had the title mashiach, the anointed one, but Jesus the Christ. He alone is King of kings and Lord of lords: the king who governs the universe, and rules in the hearts of his followers; the prophet, to instruct men in the way wherein they should go; and the great high priest, to make atonement for their sins. Hence he is called the Messias, a corruption of the word המשיח hammashiach, The anointed One, in Hebrew; which gave birth to ὁ Χριστος, ho Christos, which has precisely the same signification in Greek. Of him, Melchizedek, Abraham, Aaron, David, and others were illustrious types. But none of these had the title of The Messiah, or The Anointed of God. This does, and ever will, belong exclusively to Jesus the Christ.

Then thou shall take the anointing oil, After ordered to be made of principal spices, myrrh, cinnamon, calamus, cassia, and oil olive, Exodus 30:23.
and pour it upon his head, and anoint him; this was done, according to Jarchi, in the form of the letter "chi" as before; the oil was put upon his head and between his eyebrows, and he joined them with his finger: Aben Ezra thinks this was done before the mitre was put upon his head, for upon the head was the oil only poured; but Nachmanides was of opinion that the mitre was so folded about the head that the middle of the head was open, and upon that the oil was poured; and so the Talmudists say (x) that his (the high priest's) hair was seen between the plate of gold and the mitre; but however this was, it seems plain from the text that this anointing was after the mitre was put on, and the priest habited with all his garments; and it is also as clear a case, that the ointment was poured on his head, which ran down to his beard, Psalm 133:2, and I see no difficulty in supposing that the mitre and crown might be taken off again while the ceremony of anointing was performed. This unction denotes the investiture of Christ with his office in eternity, who is said to be anointed so early, Proverbs 8:22, and the donation of the Spirit to him in time, without measure; with which he is said to be anointed, both at his incarnation and at his baptism, and also at his ascension to heaven, and hence comes the name of the Messiah, which signifies anointed; and so his people, his priests, are anointed of God, with an unction from him, with the oil of grace, with the graces of the Spirit, which is necessary for their instruction, for the presentation of themselves to as an holy sacrifice, and to make them meet for the heavenly glory.
(x) T. Bab. Zebachim, fol. 19. 1.

The high priest was to be anointed with the holy anointing oil - That the church might be filled with the sweet favour of his administrations, and in token of the pouring out of the Spirit upon him, to qualify him for his work.